In areas that get snow regularly in the winter time, it is common practice to have additional asphalt past the usable surface(read edge line) that is called a snow strip. In order to enhance the ability to see these edge lights(at least on taxiways) they add reflective sticks to the light bases that will illuminate when light is shined on them. They will also break off maintaining the concept of frangibility in the safety areas.
For resurfacing and new construction, the FAA recommends airports in the "snow belts" to reconfigure the edge lights away from the edge line. This serves two purposes. The first has to do with height of edge lights. You have a transtional height that must be adhered to, whether it's placement of lights, wig wags, etc. in regards to engine clearance for aircraft. Remember, and aircraft does not have to always follow the centerline, it just has to stay inside the edge lines in order to be on the taxiway. The distances and heights for the lights are as follows: adjacent to the edge line, they start out at 14 inches high. For every 1 ft away from the edge line the height can go up 1 inch. The optimal spacing from the centerline is at 10 ft. That means the light can be another 10 inches higher for visibility purposes. The second reason they move the lights off the edge line is so you can plow the edge line and remove significant amounts of snow, etc. from the painted surface. It probably won't make a big difference for a day or two, but you will be able to see the edge lines a lot quicker than if you didn't do this. My airport plows up to the edge lights and makes a "back cut" with another plow and pushes the snow away from the lights to reduce any buildup around them, increasing visibility. As far as signs and other objects, we've dug them out by machine or at least attempt to not bury them, knowing that they help pilots get from point a to point b on the airport. Anything that becomes obscured, destroyed or damaged, we NOTAM out for accuracy. Airports will also pre treat, depending on the projected weather forcasts, in order to reduce icing and buildup near freezing conditions.
Some larger airports untilize low visibilty centerline lights that help pilots stay in the center of the taxiways and they are quite bright. Also, an airport will be a mess during a snow event regardless of how good a job can be done. Sometimes, it's just a matter of the snow coming down faster than the workers can remove it.