As far as I know, these browsers do not support programmed reloading, however it can easily be accomplished by using a terminal multiplexer like tmux. For example if you start the browser in one terminal like this:

tmux new-session -s browse 'w3m google.com'

Then you can send commands to it from a script or another terminal with the send-keys command. So to make w3m reload the current page do this:

tmux send-keys -t browse R