Before I start… Hello, I am vikingen, aka Butter, and I am an unofficial expert on Iceland. The actual country and nation. I'm not just making this up. I have been in love with Iceland for about six or seven years, have been called an 'honorary Icelander' by one Icelandic friend, been told by another Icelandic friend that I know everything there is to know about Iceland (I disagree, but I'm pretty darn close), and twice been actually mistaken for an Icelander online by other actual Icelanders. I think I have the right to complain a little bit here.
Disclaimer: Usually, I'm the type that thinks you should be able to interpret a fictional character however you like, but I also think you should stop to think a little when you get into Hetalia (or any other medium that portrays actual human beings). If you're told you're doing it wrong and presented with the information to back that up, as I'm about to do, I only ask that you consider what's being said. The Hetalia characters might just be kawaii babies to you, but consider that each one represents an actual group of people who can and have every right to take offense at your actions. Consider how Himaruya himself is very dainty with what he does, and while he may not be 100% accurate in everything he does, he does actually try and does actual research. Please at least do that much. I don't think you should learn everything about every single nation represented in Hetalia, but you should attempt to not be wrong. It's very easy to become offensive in this area. Also, if you really, really love that character as much as you say, I mean, isn't it a bit nice to learn about the actual people they represent? Really? It's not like that character was just sucked out of someone's imagination, that character actually is based on something in real life. (I'll raise my hand that the reason I know so much about Estonia is because I love the Hetalia character)
Now there's lots of common characterizations I disagree with in the fandom just for Iceland, but I'm specifically addressing one right now: the way everyone wants to make him depressed as if it's a foregone conclusion. My first point will be that depression is an actual issue that millions of people deal with, not something to be taken lightly. As someone who has done amateur studies in psychiatry (as well as having a host of actual psychological issues), I assure you that Iceland does not display significant signs of depression in any of canon, nor does the culture lend itself to the misconception either (I'll get into this below). By joking about how depressed you think he is, you're not only assigning a serious mental illness to hundreds of thousands of people who make up the Icelandic nation, but you're making light of the many more whose lives are actually destroyed by said illness. I'm not saying you should never portray him as depressive, because then I would be reprimanding myself as I've written a human!AU in which he has dysthymia (a form of depression). What I'm saying is that you should consider what you're getting into before such a serious portrayal, and do not lose sight of the fact that you're in territory that is possibly offensive to many, many people. (Yes, I am also one of those Sherlock fans that constantly complains about the Sherlock fandom's treatment of mental illness.)
Now to explain why he shouldn't be depressive in-universe, modern day. Iceland is consistently one of the happiest nations on earth. If that's not enough, Iceland was named the UN's most desirable place to live a few years back. And my trump card: Sixty years ago, the majority of the Icelandic population were dirt poor and a lot of the country slums. In less than half a century, the country raised itself up from living in cardboard boxes, to being one of the most developed nations in the world, yes, even more developed than the United States. Iceland's history is traumatic and tragic, if you honestly think he can still be so sad after coming so far, achieving so much, and being so ridiculously proud of himself (actual fact, Icelanders are one of the most patriotic nations on earth, or as a friend said (paraphrasal) 'We just love shoving as much information about Iceland down other people's throats because we're that in love with our country' and one of the things they're proudest of is that they've come so far in so short a time), then I don't know what you see.
If you're going to use the history to make him depressed, then please make every single nation alive as depressed, because there really is no country on this earth that has not suffered tremendously.
If you want an excuse for a depressive!Aisu, I suggest the late eighteenth century/early nineteenth century, when the people were starving, forced to sell all they had to survive, and recovering from the deadliest volcanic eruption in recorded history. The nation was more than half dead, and that's a good a reason as any to be depressed.
If anyone brings up his constantly grumpy little face, I'll smack them with a noodle that spells out 'Icelanders are a people of fire and ice: they're cold to strangers, critical of friends and loved ones, yet they're also some of the sweetest, friendliest people I've ever known.' Himaruya was entirely accurate making him a kuudere. He's cold to people (not depressed), but underneath he's warm and passionate. No one is a one-dimensional trope, please expand your characterization.
While I'm at it, can we stop making him forever alone? While it's true that he doesn't have to be really close to the Nordics (after all, they tend to leave him out of things (plz Hima stop beating this dead horse), but actual Icelanders tend to not really care about what the other Nordics do either), Iceland has good, if not great relations with a lot of other nations. Russia, Netherlands, Japan, Latvia, Estonia, Lithuania, America, even Germany. You can even go beyond politics and cultural exchange to personal things. Hey, with all the sheep, extreme sports and volcanoes he's got in common with New Zealand, they could be best friends! Seriously. Run with it. Real Icelanders are sweethearts when you get to know them and are tremendously loyal friends, there's no real life reason he can't have relationships outside of the Nordics.
Lastly, I shall not leaving you hanging after shredding everything apart. Some ideas for an accurate and non-offensive characterization of Iceland can be found in the real national stereotypes. I already mentioned fire and ice, and the extreme nationalism (borderline narcissistic Icey, anyone?), but what about all of the fun adventure-type things in Iceland? Spelunking, white water rafting, cliff diving, I could go on. These are the things that Iceland is known for. What about all of the slightly nutty artists? What about the huldufólk and deep connections to Norse traditions? What about the strong rebellious tendencies that actually founded the nation by driving many of the original settlers from Norway in protest?
You don't have to characterize Iceland exactly as I do, but I only ask that you take what I have to say with a grain of salt and rethink your ideas. After all, the more you know…