Interesting topic!
I would be a bosmer, of course. My in-game character is supposed to be me, but she doesn't do everything I would likely do if I actually lived there.
So, I would probably be an adventurer, until I take an arrow in the I might be a random explorer/adventurer as a side job but no killing, and nothing dangerous or war-related. And yep--no snow for me either! >P I'd live in a hand-built cabin just outside of Riverwood, and do odd jobs like working at the lumber mill (and into my colleague Faendy's heart!). I'd often visit Faendal's house like a creeper, and discuss nature-y things: though I know we could never be together because I just can't accept an avid hunter like Camilla can.
But I know I wouldn't make enough money with a boring village life, and I'd have to do something else. So I would make a weekly commute to Whiterun and advise the Jarl on ecological matters (and brag in Nazeem's face about it), and would stay in Jorrvaskr for the duration of each weekend I'm there, available for anyone to consult with me about veterinary medical matters. I would be an expert in restoration magic and would use spells (but also science) to heal the townsfolks' pets. I would always be on-call to travel to other towns in case of emergencies, too. And thus I would need a fast little horsie to keep me company, and a personal courier/secretary to keep me alert of when I'm needed. To pay this person, I would also further supplement my income harvesting crops for the farmers around Whiterun, and starting my own garden outside my house back in Riverwood. I would grow rare organic fruits, and nirnroots. On my commute, I would also collect flowers and herbs and make potions to sell while in Whiterun.
I would still go on occasional adventures, though. I would have a pet dog and pet skeever, and bring my companions with me to explore caves and dungeons we come across. I would leave if we encounter bandits or bears or trolls, but I have no problem fighting draugrs and skeletons which are already dead. So we would clear out any places with only undead and I would loot all the money and books there, and take them back to cover the walls of my library-cabin out of Riverwood.
I wouldn't normally carry any weapons but a fine steel dagger (enchanted with a magic paralysis effect), but when adventuring I'd primarily be an archer, and also have a small, light sword and shield. I'd use a few small destruction spells--probably ice--but I probably wouldn't be much good with non-healing magic. I'd specialize in light armor, and none of it would consist of leather, fur, or hide. It'd take a few years to perfect, but I'd create my own light armor out of plant plastics, and it would be sturdy and clear, and--along with fine chainmail--be concealed under my normal clothes as if I weren't wearing anything. My normal work clothes would be hand-dyed linen robes for healing and a two piece outfit for walking. I'd be almost the only girl in Skyrim to regularly wear pants.
I would not be good with any heavy stuff at all, but I'd be very quick-thinking, light, sneaky, quiet, and fast. But I'd wear out easily so I guess 't sucks for me if an angry mammoth's in hot pursuit or something. xD
I would not be dragonborn, but I'd like to briefly study at the College of Winterhold and then climb the 7000 steps to see if the greybeards would accept me as an apprentice, housecarl, or even errand-girl.