Last winter I used an 80's road bike with a fairly aggressive geometry. It had barely enough clearance for 35 mm studded tires and I mean barely. I considered it an experiment because I wasn't comfortable with that small amount of clearance.

Anyway, being down lower felt good from a center of gravity standpoint but having that much weight on the front wheel and fairly narrow handle bars made it prone to having the front wheel dig in and skids that were hard to recover from.

I liked having drops enough that I decided they're something I still wanted on a winter bike but I felt I needed something that was designed for offroad use since the more challenging winter riding I do is like riding offroad. I ended up putting cyclocross type bars on a 90's 700c mountain bike and have been pretty happy with the setup.

A more upright bike may indeed be more stable, I don't know. I do know that winter winds can be a PITA and I'd prefer not to be too upright.