How to stop cold air entering through the breaker box
What you are looking for is duct seal. You can pick it up at most home centers. This will seal the external conduit, where the power line enters the house.

For sealing the studs, you could get a can of insulating foam (Great Stuff or another brand). The Firestop type would be your best bet.

Any place wires penetrate your siding, you should seal them with an outdoor/weatherproof caulk.

I wouldn't recommend sticking anything into the breakouts on the box itself. If you want to, you can get some better sealing bushings for these, but you'll have to pull the wires and reconnect them. Sealing the outside conduit will give you the best bang for your buck.

You should also investigate the outside. It looks like the wired are coming straight in from the back, rather than through a mast. If there are any other boxes on the back (like your meter) you should caulk around the outside where the box meets the siding.