mutt 1.5.18 works fine with Cygwin (as I just discovered). Building it from source I used

./configure --prefix=$HOME/local/stow/mutt --enable-imap --with-homespool --with-ssl=/usr --enable-hcache --enable-locales-fix

This is assuming you installed the openssl-libs and openssl-devel packages (those can be installed using Cygwins own installer .exe). For header-caching (you really want it when using IMAP) you’re also gonna need some version of berkeley-db, which can also be installed using the Cygwin setup.exe.

msmtp (an SMTP-client which can be used in conjunction with mutt when sending mails over a server which uses TLS/SSL) works equally fine. With version 1.4.16 just do

./configure --prefix=$HOME/local/stow/msmtp --with-libgnutls-prefix=/usr

GNU screen is available as a Cygwin-package (4.0.3) but if, like me, you want 256 colors (and with a spiffy vim-theme you do ;) you have to fall back on building it yourself. You have to apply two patches though: Patch 1 (found here) and Patch 2 (found here). After that

./configure --prefix=$HOME/local/stow/screen --enable-colors256

should do the trick. To actually get 256 colors working use this in your .screenrc:

# terminfo and termcap for nice 256 color terminal
# allow bold colors - necessary for some reason
attrcolor b ".I"
# tell screen how to set colors. AB = background, AF=foreground
termcapinfo rxvt 'Co#256:AB=\E[48;5;%dm:AF=\E[38;5;%dm'
# erase background with current bg color
defbce "on"

Careful! If your TERM (the one you start screen with) is not rxvt then you need to adjust that. To see if 256 colors work I use this script (found here).