If you're talking about the foreground and background colors of the text within the terminal itself, it is certainly possible. Those colors are produced by ANSI escape codes, which are not specific to either Konsole or gnome-terminal; they work on any terminal program that supports color at all. For a complete list of the codes, see Wikipedia.
To actually use the color codes, you write a sequence of the form
\[\033[01;31m\]. That example changes the text foreground color to bright red (
01 is bright,
31 is red) until it encounters another color change. To use a different color, change the 31 to any number from 30-37 (for foreground colors) or 40-47 (for background colors). As an example, my shell prompt is set by
export PS1="\[\033[01;32m\]\u@\h\[\033[01;34m\] \W \[\033[01;37m\]\$\[\033[00m\] "
which gives me username@host in green, working directory in blue, and then a literal
$ in yellow. The
\[\033[00m\] at the end is a reset code which clears whatever foreground/background colors have been set.
By the way, the actual color that, say,
31 corresponds to is normally red, but it can be changed. I know that Konsole allows you to set the ANSI color palette, I'm not sure if gnome-terminal has the same ability.