Are cooling fan suppose to be on in the winter or no because my is not on? I know this may sound dumb but its bugging me.

 

The fans are simply controlled by engine temp. Cold outside temp will keep the engine temp down reducing the use of the engine fan.

 

It just depends on how cold. Even though the rad temps will be down, your thermostat should still work properly to get the motor up to temp

 

I recently changed the thermostat on my 93 Civic DX and so had to do an air purge of the cooling system afterwards. From cold idle to full warmup (= cooling fan comes on twice) required 40 minutes at an ambient temperature of 55 degrees F. I have timed this many times with my two Civics, and 20-50 minutes is always necessary (20 minutes being in the heat of summer). I do not think my fan otherwise comes on in winter temps when I am driving. The cool winter-y air flowing over the radiator keeps the system plenty cool.

If you are very concerned, there are ways to test the fan and fan relay.