tires -
someone has new snow tires sized 205/50R/16.
can these fit when my tires NOW are 175/65/15...
would i need new rims for the snow tires?

 

No, you can not mount 16" tires on 15" wheels, or vice-versa.

You would need new wheels.

 

Any tire that is 205/50-16 used for a MINI should be mounted on a wheel that is 16" diameter and 5.5" to 7.5" wide for a correct fit, it will be OK. MINI stock wheel is 16x6.5". Many aftermarket wheels are 16x7". While this tire size can be used for a MINI in most weather, it's not the optimal size for a true snow tire, usually something less wide would cut through deep snow better. Nevertheless it can be used in the winter with light snow.

Your base cooper stock wheels are 15x5.5" and fit the 175/65-15 tires you have. 15" diameter wheels only fit tires with a size ending in 15. You are not limited to that size tire on those stock wheels.

185/65-15, 195/60-15 and 205/55-15 all will fit and work. The first number is the width of the tire tread in mm, the second number is the sidewall aspect ratio, with larger number being taller more comfortable flexible sidewall and last number the diameter of the wheel it fits.