Help! Recommend boots for winter camping and hiking.

Expect a maximum low of -20f but up to a 15f high. Expecting to trudge through the snow, possibly dogsledding, and a mix between moderate activity (day hikes) and low activity around camp.

The problem is, I can't afford two pairs of boots (one for low activity and one for high activity). My budget is $200, but can look at higher prices with the potential to buy them used.

Can't rely on mukluks either, as there is a potential for slush/wet.

Do you see my dilemma, and can you offer any suggestions? I have been trying to research this for months. I am a woman, expecting to size up 1.5-2 sizes to accommodate socks. Help!