Today, a mason installed a chimney cap for us while it was snowing. I
saw he was using adhesive. I don't know what kind.

I asked him that whether it's okay to use adhesive when it's cold (32F)
and wet. He said the sealer he used is okay. Is there such kind sealer
that can be used in old and wet surface?

It'll be okay. Tom

hmmmmmmm.....my chimney flue caps had screws to tightened snug at the
corners. I never heard of gluing one on.
Debi