first I would check the pump belt to make sure it is intact.
There will be a inspection hole.
Is the cable still functioning.
inspect to see it the hose off the oil pump is in good shape feeding the fuel pump, then the hose leading from the fuel pump to the bearings.
I dont know of to much that can go wrong with the oil pump itself, but then again I have never taken one apart.
Was this the first time out on the sled this year?
Where the carbs remove, taken apart and cleaned?
I seen a lot of problems arise when the jetting gets plugged.
I am not sure how much experience you have with snowmobiles and dont want to come across as being a know it all cause that I am far from that.
If in doubt I have read where sledders will run a tank of mixed fuel and also run with the oil reserve full and then check the oil consumption when you run through a tank of fuel. or say 25 liters of gas to 500 ml oil. Your should see at least 500 ml oil used out of the reserve.
Good luck.