The OEM tire size for my wheels is 225/75/R15. Can I use 205/75/R15 tires on these wheels?
They will fit your existing rims, yes. However, if your OEM size is 225/75/R15 then a 205/75/R15 would more than likely not have the adequate load carrying capability necessary for your vehicle.
The tires will fit on the rim but the overall height of the tire will be smaller ( giving you the wrong speed on your speedometer, reading higher than actual speed ) and the 205 tires' load index may be too low for your vehicle which could result in a tire failure ( cannot support the weight of the vehicle )
I want to use skinnier tires for better performance in snowy conditions.