When the water unfreezes you can basically drain it into a chamber further underground and either let your dwarves drink directly from that as an underground lake or pipe that into a well.
As for the initial question, its not too bad to start in a snowy zone, in fact as another said I actually like it when seasons pass, if you get immersed into the game as I do its nice to hunker down when a blizzard comes in your shelter (and seeing everything up top being buried by snow). The only notable danger is (as has been said) being on top of a river/lake when it unfreezes (I lost two wagons that way), the first thing to do is go down one Z-Level and check to see where the water is so you don't build on it and if you are parked on it unload your stuff.
That all said it's not really that much harder, just makes your water collection a bit trickier (you want to collect it when you can cause when you need it it might be frozen) and there is a slight danger of drowning.
Back in the pre-cavern version perminantely frozen spots used to be very hard because collecting water (which was, for a few releases, necessary to farm underground) was difficult (glacier) to impossible (tundra). These days you only need water as a backup in case you run out of booze or if somebody gets hurt/sick, and if you really need it odds are you can find it underground.
-MB