The improvement would be at consumption end - decreased horse need for fodder through decreased horse labor and horse numbers
It's a relatively minor saving on the domestic front - given that in normal crop rotation in the 20th century fields have to be left in grass anyway I.E. cut for hay Certainly not enough to warrant the initial investment.
Do you think that the care of traction horses is trivial?
Not trivial - but the German army would have a relatively high percentage of people from rural/agricultural backgrounds anyway...but the care and feeding of steam traction engines is as black an art ( ) as stoking/running the engine room of a steamship, or crewing a steam railway locomotive. It's a skill that needs to be taught/acquired, and developed.
A faster Axis advance means most of the Soviet tank industry would be overrun rather than evacuated. This means that there wouldn't be that many of those pesky rattly-shooty-tanky thingies, in particular of the 30+ and 40+ tonners that axis tankers found so annoying.
I'm afraid there would be - for don't forget that by the time of the fighting around Moscow...anything up to 25% of Russian tanks - particularly the heavier ones - weren't of Russian construction anyway