I have owned a WRX hatch and an 07 STI. They are good in the snow, you shouldn't have any problem controling either car. Don't let the adjustable diff sway you though, it makes very little difference in the driving expirience, esspecially in the snow. My opinion is that the car handles more predictably in the bad weather with the setting on auto. I have driven an 09 WRX and the difference between it and the 07 STI is not all that much as far as power, STI has a little more power at highway speeds, but really, the only difference is the 6spd which is nice.
On another note, if you do not mind the brand too much, you should go and drive a Mitsubishi EVO X GSR. I have always been a fan of the STI, but when i drove the EVO X it was night and day. It's really sad to say, but the EVO X GSR feels much better in all weather and all driving situations when i compare it to the STI. Its ultimately something you need to find out yourself, but i highly reccomend the EVO. Its what i currently drive and its great bang for the buck, you can pick one up for around 32k these days.
If you are looking for a low payment however, NOTHING beats the WRX's bang for the buck. It's really cheap for what it is, these days the STI is really overpriced. The pre 08 models could be had for less than 32k new, and the new WRXs perform almost just as well as those for 5-6k less.