Dd has a costume that has almost no sleeves.Just a shirt inside might not be warm enough so does that mean we have to change for long sleeves or is there another way out? I mean almost everything we saw was with short sleeves. She didn't like the only one with long sleeves.
We just tossed on good quality (and snug fitting) long underwear under my daughter's costumes when she was young. Now she plans on it being cold and plans her costume accordingly.
Being cold might make the time miserable, but she won't get sick from it- is there an underlying respiratory or immune issue causing concern? If that is the case, I would probably scrap too much outdoor/in public/lots of germs exposure anyway.