Is safari open in Jim Corbett?

Yes.
Safari in Jim Corbett National Park remains open throughout the year, at least in two tourism zones.
Following is the zone wise details :-
1) Dhikala – 15th November to 15th June
2) Durgadevi – 15th November to 15th June
3) Bijrani – 15th October to 30th June
4) Sitabani – 01st October to 30th June
5) Jhirna – Throughout the year
6) Dhela – Throughout the year
However it is advised to check weather prediction as safari in Corbett National can be cancelled without any prior notice in case of heavy rain.