Hello!
Unfortunately, there was a small warming for a couple of days, which means that daytime temperatures are 12-15 Celsius and nighttime temperatures are 3-4. This morning it was -1 Celsius, which surprised me because the forecast was 2-3 degrees. The ends of the shoots on maples started to turn gray and dry in the afternoon, this affects a quarter or less than half of them. How big can the problem be and how much will it affect spring shoots?     

Maples can take a lot more than -1 degrees. I would not worry.

Why did the buds suddenly start to dry up?
 

I think that is just a thin layer of skin drying up. Possibly from the tree getting ready to start pushing leafs soon. If the buds fail, they shrivel. Yours is plumb and full of water. Do not worry.