Looks like at most 5 MB uncompressed, i.e. about a 1% increase in storage requirements.
(I just checked this based on the files required by a previous attempt at this, RFC: Add cygwin mintty to windows binary distribution. by twadleigh · Pull Request #12879 · JuliaLang/julia · GitHub, which installs the Cygwin mintty. It could probably be cut down further, e.g I’m guessing the Msys-based mintty — the same thing that “git bash” uses — is smaller. mintty.exe itself is less than 1 MB, the rest is system libraries.)