Just picked up a DS650! Help/Info needed

I bought a 2002 DS650 quad was in really decent shape.

I changed the oil, adjusted brakes....etc

Well, today I went riding, quad was popping out of the intake, coolant leaking from somewhere...etc

I found the boot from the carb to the head was put on wrong so it came apart....new clamps sealed it right up...fixed the rough idle/popping.

I filled the coolant to the top of the over flow bottle...my mistake so I drained some coolant and fixed that issue.....

Well, the fan was coming on.....quad didnt seem to hot...coolant was full, oil was full and clean.....

Don't know the exact temp outside but its snowing....is it normal for the fan to come on in these conditions?

The temp light was not on.....

I know it works because both the N light and the RED light is on but as soon as I start it, it shuts off..

HELP!