Pushing in reverse is also dependent upon the implement you're using. A standard blade is curved forward and will normally ride up over small items (bumps).
A box blade like I use has both a front and a rear blade- the rear curves towards the back. With this type of blade, it is important to keep an eye on the tilt angle (using hydraulic top link).
When tilted back, in reverse it will tend to dig. Tilted forward will tend to ride up and over.
Here's what I do in this deep snow.
When pushing deep snow back and out of the way, I tilt forward and slowly raise the box blade as the tractor slows due to traction or amt of snow. This is a fast push.
Then I follow up with blade tilted back and slower to scrape the snow from the surface.
I also push straight a ways then steer it off to the side. I didn't change it over for the straight, pivot blade, so gotta use what I have
I've also found the box blade is a bit heavier than the old straight blade- better traction in the snow.
I do drag forward for tight spots, but you can only drag so much going forwards.
Hope this helps!
- JC