It's funny, I actually love WIndhelm. It's my primary residence and I enjoy wandering around the city. But then I prefer winter over summer, and tend to like my scenery a little more sparse and rugged. I feel like I'm in a place with some genuine history.
Windhelm is my 2nd favorite city (the favorite is Whiterun, better weather there). I'm not too fond of the snow and ice (of course, the weather and climate is symbolic, surely there are seasons even though they're not shown in the game, and perhaps Windhelm has beautiful summers), but I really like the architecture and city plan. It feels like a true medieval city, where narrow alleys suddenly open up into market places (and had Windhelm been a real medieval, European city, there would of course have been a gothic cathedral where Candlehearth Hall are).
Back on topic: No, I don't think being a jarl is such a great idea, just because it would keep you from adventuring. But being able to hand out jobs when you're head of something (Lyn's idea is excellent), and being acknowledge for what you are (by your guildmembers and in some cases, like when you're Harbinger, by jarls and their stewards and housecarls - NOT by guards whispering "Hail Sithis"!) would be great.