Why doesn't my toilet flush completely outside summer months?
This screams frozen vent stack.

To keep your drains flowing, you need to equalize the pressure. The problem is your sewer lines contain harmful gasses you don't want in your house. As such, you have a vent stack, a common drain pipe that allows gasses to vent out of the roof.

In deep winter (i.e. well below freezing, which is common in Michigan) what can happen is that the warm(er) water has some vapors that will head up the stack. Due to the extreme cold, the vapor condenses as it leaves the top of the stack. It then strikes the cold pipe, freezing to it. And now this makes for a nice perch for snow (image source)



There's a couple of things to do


Insulate the vent stack pipe inside your attic. This helps a bit in that the water vapor loses less heat as it ascends.
Install something designed to keep the vapor from freezing to the top of the pipe. There's a number of products that do that by either passively absorbing heat from inside your home and transferring it up, or by being made of material that absorbs solar heat to keep the surface above freezing. You can also install a traditional pipe heater materials at the top.