Mavrik, in general wider tires should make the handling of the Savage "less precise" because of the width of the Savage rim.  A relatively thin rim (which the Savage has)with fat tires will create less stable side walls.  (BTW, I think the stock Savage tire is too wide to begin with.)

How much will the change be?  Not too much for small changes, but may be noticable to the highly tuned rear-end.  

Some on this site have reported improved handling and feel with thinner tires front and back.