Change terminal colour based on SSH session

Yes, you can by changing the PS1 value in .bashrc file on every hostname where you are connecting with ssh.

See this answer to view how to costumize as you like the bash changing the PS1 value.

ssh colored

On my machine (radu@Radu) I have in .bashrc:

PS1='${debian_chroot:+($debian_chroot)}\[\033[01;35m\]\u@\h\[\033[00m\]:\[\033[01;34m\] \w\[\033[01;37m\] > '

On the hosted machine (radu@ubuntu) I have:

PS1='${debian_chroot:+($debian_chroot)}\[\033[01;35;40m\]\u@ubuntu\[\033[00;40m\]:\[\033[01;34;40m\] \w\[\033[01;32;40m\] > '