The 195/60/14 actually has a taller sidewall and may increase the symptoms you are trying to avoid. The performance winters are still very capable and exhibit the characteristics you seem to be describing. I think you would be pleasantly surprised.
Wouldn't a tire size 185/65/14 have a taller sidewall?
Yeah, after a few suggestions here, I will be looking into a winter performance tire.
Thanks again. 
I think morty means to say that a 195/60R14 has a taller sidewall than a 175/65R14.
Good luck on your search, and let us know how it all turns out.
Yeah, I got confused. I thought he was comparing it to the 185/65/14 tire size, not my current 175/65/14.
I will let you guys know what I decide to do.
Thanks again.