Old incandescent bulbs actually used to melt snow for streetlight and this had to be addressed when switching to LEDs.

In a large fridge a small incandescent lightbulb won’t make much difference since it turns off when the door closes and would have a relatively small thermal mass, which I think is what you’re saying. That said I don’t think it’s accurate to say that “all of the heat is in the filament.” Heat spreads, and it will leave the light bulb. If you have ever touched an incandescent light bulb that is on you would have no doubts about this! Easy bake ovens used to use incandescent light bulbs to cook things, people leave their oven lights on to keep their oven warmer to let bread rise. Larger incandescent light bulbs can absolutely warm up a full sized room, 60W or 100W is a fair amount of heat. There are stories about extremely temperature controlled rooms where they would turn on a 100W bulb when a person leaves it because a person produces about 100W of heat.