I doubt that antibiotics are needed for the red tips of the toes. There doesn’t appear to be infection. It may just be a symptom of the frostbite. In the picture in this link—frostbitten toes, you will see the pink swollen area above the frostbite that is very common:
https://the-chicken-chick.com/frostbit-in-backyard-chickens-causes/
https://the-chicken-chick.com/frostbit-in-backyard-chickens-causes/