I would have to second the high winds comment. I think the best solution would be a quality 3 season tent, which should be in your price range, coupled with a decent sleep system (sleeping pad and bag) and a tarp (or two).
The problem with smaller tents (e.g., versus wall tents) IMO is the lack of airflow that would otherwise help to keep down the moisture, condensation, and general clammy environment.
I have a four-season mountaineering tent that I have camped on snow in and there is so much less ventilation than in my three-season tent. Even then, we slept with all windows opened and woke to condensation frozen all on the inside of the tent. When it warmed, while we were hiking up the mountain, it had rained all over our bags. Just something to consider.
If you were to have one tarp as a ground cloth under a three-season tent and another as an oversize rain fly positioned about a foot above the top of the tent, you could keep the tent windows unzipped and maximize airflow. The other tarp can be used as a ground cloth to keep water from seeping in from the ground.