It is pretty hard to beat a Tacoma 4 cylinder 4x4 truck in reliability and in snow. That’s my daily commuter. Throw some sandbags in the bed when it snows and you’re unstoppable (in a good way assuming you’re not on ice. Then you’re just over your head).
It is probably equally hard to find one for 3K.
I am very partial towards Subaru but you’ll have a pretty hard time finding a good one that has no issues and doesn’t require some work for that price.