Nice rig! RE: using float and plowing with a bucket. It looks like your bucket has a factory edge bolted to the bottom edge? Regardless, you want to be careful to not dig, regardless of effect on your lawn and mower in the spring, you want to keep from having the tractor's forward momentum force the FEL in a direction other than where you are headed when/if the bucket edge digs in unexpectedly. This could easily cause difficult to repair wracking to your loader arms. FELs are meant to lift way more than push, especially if they encounter immovable objects like rocks, frozen ground, etc. Better to angle the leading edge up away from grade to allow the bucket to, in most instances, in conjunction with float use, to float over the first few inches of snow base. You can always, CAREFULLY backdrag the bucket edge, again with caution, to bring down the snow base to an acceptable level.
I suggest operating in lowest gear possible to develop technique and then over time you will have a system down that does least harm to your machine. Remember, tractor is a push/pull machine for things that will move with forcing it to stop.