This brings back memories. These snowmen are probably around 55 years old. Their noses used to blink in no particular order (using 3, C batteries), but years ago the lights stopped working. I called and visited about every electronics store in the area, but no one had replacement bulbs that blinked. I put in some bulbs that fit the sockets, but the light is steady now.
I finally had the enthusiasm to take it apart. This usually results with the object not working afterwards. Unfortunately, I don't have any C batteries on hand and am reluctant to buy any just to test the figurine. The end lights are original, the center was a replacement. After that the lights didn't blink anymore.