Usually, these things change from year to year depending on how hot it is in April and May. As a general rule, most of these high altitude areas (i.e. 4000m+) open around June 10. That goes for Babusar, Deosai, and Khunjerab. At least that is the safe date I have been told by local drivers over the years.
This year, it is already getting hot and we are only at the end of March. If snow spells do not return, then yes it would be possible but since this id dependant on weather, it is hard to be exact but just make rough estimates.