Stock size is 215/55R17. Would 215/65R16 be okay to be used as winter tires for couple months a year ?

Seems you are a bit late, snow tires are as much about temp as they are about snow. Can`t say, don`t remember the size of my snows. They go on in October and come off in March.

Assuming a sedan, but that seems a bit taller than we would normally recommend for the car.