There is no way to clear the ICS window now. I am also not sure why people would want to do that. I included a 'clear' button in the Chat Windows; this was mainly intended for using when you switch the handle in the Chat-Partner field, so that you don't keep the discussion with the previous chat partner there if you don't want to. (When chatting with an individual, no names are printed.)
I guess that by not specifying the ICS text field as ES_READONLY in the winboard.rc file, people would be abe to do any editing they want in that window. Just select everything with Ctrl+A, and pres DEL, and it is cleared. WinBoard does not really use any of the text there. (Except when you right-click a word, it uses it in the context menu. But it just reads it back from whatever was there in the text window, it does not make any logical connection with something that was received. It is just used as a source of text you can click.) But I still don't see any legitimacy for the wish to do that.