Cooper is absolutely correct, the temperature in your house can effect the temperatures inside your Dragon's tank of course, but as long as you use the appropriate wattage of Basking Bulb inside his tank to keep his temperature zones/gradient within the correct ranges for a Bearded Dragon, this keeps him in the correct environment. However, even if his tank is within the correct temperature zones and your house temperature isn't effecting his tank temperatures at all, if you live in a place that has seasons, your dragon still knows that it's winter due to the change in Barometric Pressure outside. This is the only reason that reptiles kept in captivity and kept in proper temperature zones that are constant throughout the year STILL sometimes go into Brumation. They certainly don't HAVE to Brumate like they do in the wild, their tank temperatures/lighting are keeping them warm and able to properly digest their food and absorb the nutrition from the food, so unlike Dragons in the wild they don't need to go into Brumation to survive. However, since the change in Barometric Pressure outside is telling them that it's winter and since the instinct to Brumate is innate, no matter what the environment that they're living in is like or whether Bruamtion is necessary in that artificial environment to survive, some of them still do Brumate. So whether they Brumate or not has nothing to do with their artificial environment in captivity. That being said, there are obviously things you can do to knock them out of Brumation or to keep them in Brumation, but as far as them naturally wanting to Brumate, that is triggered by the Barometric Pressure outside.
As far as the lighting in your house goes, the actual lighting isn't going to effect anything as long as your Dragon is under the proper lighting inside his tank that he's under. However, if you have his tank/enclosure located near a window or door that allows a lot of sunlight to get through to him, especially if he's in a glass tank, then this can obviously cause serious issues for his tank environment, such as causing his temperature inside his tank to rise. Many Dragons and other reptiles/amphibians have died because their tanks were too close to a window or right in front of a window, and they basically were "cooked" by the sunlight and the rise in tank temperatures. So you always want to make sure that your Dragon's tank is not located in a spot where natural sunlight can get into his tank and effect his temperatures. If they are exposed to high temperatures for a long period of time, if it doesn't kill them and they recover from the acute dehydration and heat exhaustion/stroke, it can actually permanently effect their ability to thermoregulate. But as far as the lighting in your house or the lighting from outside coming through the windows effecting whether he brumates or not, again, they already know what time of year it is, or rather what the "season" and temps are outside due to the changes in Barometric Pressure, so the lighting inside the house isn't a factor.