I know that when deeper into summer the winter insulation turns off, however this doesn't happen for Wilson's beard and it instead cancels the effect of the eyebrella's protection. I'm not sure if it is intentional to make Wilson shave his beard in summer. However, it seems odd I can wear a winter jacket and be fine, but I am not allowed to keep my luxurious beard.
I did not check, but the same could be true for Webber and Woodie's beards.
Have a full beard in summer and it will negate the protection of the eyebrella.