Does the frozen biome itself provide cooling?
The only thing that would 'produce' cooling is the wheezeworts. I don't see any in your picture, maybe because you already dug them up.
https://oxygennotincluded.gamepedia.com/Biome says that no biomes have special properties that keep them cool or hot, merely their starting temperatures.
I think what is happening is that there is a lot of tiles to soak up added heat. If you want to melt the frozen biome, try digging out the abyssalite separating it from a hot biome. Or save it for pumping to your base for cooling.