Is it possible to do a word count for a complete TeX project and not only for the current document?
No. However, on CTAN you’ll find a utility that produces a word count from the dvi file. This might be just what you are looking for: it can be more accurate than WinEdt because WinEdt does not know how certain TeX macros get expanded while dvi file contains processed text with all the words… A tool not located on CTAN is Translator’s Abacus; a Wordcount program that can count the words in html, pdf, Word, RTF, and text file – no DVI file though, but it should not cause any problems to produce an intermediary pdf file (with pdflatex) to do a word count with this program.