What kind of hive? If it is a Western Red Cedar Flow hive, you don’t need to paint it at all. You don’t even need to seal it. However, I would. I use Tung Oil 100% pure - not a blend with any chemicals. It preserves the color of the wood. If you don’t do that, the wood weathers to a silver grey, but it won’t rot. Search this forum for “tung oil” for advice on where to get it and how to apply it.
If it is pine, you need to paint it. Any exterior house paint is fine. Most people use a light colour, but you may choose camouflage colouring if you want. Don’t use red or black.
Paint or seal at least 4 weeks before you intend to install the bees, so that the paint/sealant can dry properly in your chilly climate.