No! It is not a good idea to mow your lawn with frost on the grass because the lawn mower's tires can snap the grass blades at the soil surface and so can your foot prints.
If you care about the grass, you should not walk on grass while frost is present.
Late fall, over the winter, and early spring lawn mowing tips
Frost maybe present during certain times of the year when the lawn may still need to be mowed. If you notice frost on the ground when attempting to mow your lawn in the late fall, over the winter, or early spring, you should wait until the frost melts or reschedule your mowing to a warmer day in the near future.
Frozen Grass Can Snap On Contact and Damage The Grass Plant
When things like lawn mower tires or shoes contact frozen grass blades they are likely to snap or break. This fracture could occur anywhere from the soil surface to the top of the frozen grass blade.
Remember the 1/3 rule when it comes to mowing. The 1/3 rule states that no more than 1/3 of the grass blade should be removed during a single mowing session. When more than 1/3 of the grass blade is removed it can damage the internal structure of the grass plant and cause damage or even kill the grass plant leaving bare spots.
Learn more about lawn mowing from a local lawn care company that shares tips and tricks on their website.