HDD swap from 2009 core duo to 2010 core i5

Fluid spill kiilled my late 2009 17-in core duo 2.8 GHz. HDD survivied. Bought an early 2010 refurbished 15-in core i5 but it only has a 500GB HDD and I have a terebyte HDD with 800GB used. Can I just install the old drive in the new MacBook Pro and will it boot, or will it be missing drivers? I have a complete Time Machine backup, but I don't want to reformat the 1TB HDD as I will lose everything from my Windows Bootcamp partition the was NOT backed up. Old HDD has Snow Leopard 10.6.8 What is the cleanest way to get up and running?

I'm not dead sure on this but I think you will be OK. Unless I looked up the wrong model from MacTracker that 2010 model shipped with 10.6.3. I don't think it will hurt anything on the drive to try. At worst it should just refuse to boot.