Too many variables to predict. In some cases travel on snow is faster than without it (complete coverage over talus). Timing is everything. Generally snow is harder in the early morning.

One trick (on typical early summer snow) that may help stay on the top layer rather than post-hole : firmly plant your forward foot, let it sit a split second, without jerking or pushing your foot transfer your center of gravity over your forward foot, easy up onto the foot, repeat. The split second pause lets the snow stabilize around your boot tread. This also automatically gives you a rest-step which will conserve energy.

Also, if you are regularly falling through, you may as well just stomp through right away.

If you do a lot of snow travel, you will learn to "read the snow". Experience will help you make good route choices and go faster.