a 10w bulb is hot in a small space; it can make so much heat that it can be a fire hazard, if you have wrapped it in a plastic bag and prevented air flow from removing the heat buildup.
Even your computer's modem can produce a lot of heat and melt itself down when you put it in a plastic bag and cover it.
If you wrap both pipes together in plastic (like saran wrap), the hot water pipe will keep the cold water far above freezing, and you will end up with hot water closer in temperature to non-scalding. That is a no-brainer, it will work, and if you cannot figure out any more "subtle" way to keep your cold water above freezing, do exactly that.
If your cold water pipe is wrapped separately, that is fine too, as cold water is above freezing, and the challenge is to prevent it from losing temperature so fast as to freeze. Keeping water flowing helps a lot to do that; that is the reason to drip it during cold spells. The incoming water is above freezing and the loss of temperature is not significant by the time it reaches the tap.
Wrapping the pipe in anything fluffy first before sealing air flow with continuous plastic is the best way to uncouple the heat loss from the pipe wall and the cold space around it. By adding that minor fluff, you have made a two-layered insulation, each layer of which improves the properties of the other layer.
Before adding extra heating devices like light bubs, just separate physically the pipe walls from the surrounding air, by putting anything fluffy covered by a continuous layer of air barrier. The cheapest plastic will do. The cheapest fluff will do. Used materials will do. Recycled birds' nests, and used plastic bags from a dumpster. Anything at all, as long as it stops the (cold, attic) air from touching the pipe walls.
david