A subset of the title question is: What temperature do lawns consider a frost? 32F? 30? 28? By "consider a frost" I mean get knocked back or prevented from growing. So if lawns frost at 32F, then how long do temperatures need to be >32F for the lawn to begin growing? From there I can estimate the usual "X weeks of growing from this height, the lawn needs to be mowed".
It's a complicated subject, and to some extent, depends where you are and what sort of grass you're growing. In the UK, I might cut grass in early January, if it looks like it needs it - but only if the weather is temporarily mild, or at least above 5 deg C during the day - if a frost forms that night, so long as the temperature doesn't fall below -2deg C, the grass will come to no harm, even though it's been cut.
There are differing types of frost; air, ground, grass, and so on, and these form under certain temperatures and conditions - this link, although it refers to UK weather, explains that https://www.channel4.com/news/by/liam-dutton/blogs/air-frost-ground-frost-difference. The temperatures are quoted in centrigrade, so you'll need to translate into fahrenheit.
The time not to cut grass is if the ground is actually frozen - just because there's been a frost, the ground may not be frozen - for that to happen, temperatures would have to remain below freezing day and night for a considerable period.
So if your daytime temperatures are reasonably mild, winter's almost done, and you haven't just come out of an extended period of below freezing temperatures, I'd say cut the grass if it looks like it needs it - with the blades set high, obviously.
When your grass crop looks frost covered, do not step on it. You will easily kill the crowns of some of the grass species. I've seen the footsteps of dead grasses where an owner walked out on his lawn when there was frost. Even just freezing temperatures during the early morning hours could freeze the crowns of your grass without 'frost' appearing on the lawn.
Grass should be cut once per week minimum. Twice is better. But the tough part is people do not hear 3 1/2 inches as minimum height. Use a ruler. Make sure your mower cuts no lower than 3 1/2 inches (cool season grasses only).
The problem is not frozen ground it is frozen plant material. Leaving your grass cut at 3 1/2 inches as your last mow in the fall would help keep the crowns from freezing. Grass will be fine, frozen during the winter and spring if you do not step on it. Most certainly do not put a heavy mower out there to mow!
Mow often, sharp sharp blades, but do not go lower than 3 1/2 inches. The cool season grasses have large root systems...large root systems need a minimum during the growth season 3 1/2 inches of photosynthetic top growth to make enough FOOD for the grass plant for health and surviving the winter.
Fertilizer is not food. Most lawns need at least 3 to 4 fertilizer applications that have different formulations for different seasons. Too much nitrogen applied during the fall going into the winter will cause excess new growth that will be susceptible to cold, drought and will cause conditions in your lawn that fungus will love and thrive and cause problems for your lawn.
Just never walk on frozen grass. The soil is probably frozen but it is the cold that freezes the grass and then you walk on that frozen grass that will kill the grass you stepped upon.