Can I put '05 V6 winter tires on my '01 GT?

Before considering, keep in mind that these tires are a fair bit taller than your current ones (nearly an inch and a half). I see that you've got lowering springs on your car....you'll most certainly having rubbing issues as well. The Offset is different between the SN95 wheels (30mm) and the S197 wheels (45mm).

If you can get them for nothing and try them on before taking them, go for it. Otherwise pass and wait till you find the right wheel and tire combo to suit your needs.