What a pain! Texmaker still does not have a word count feature.
I know this is far from perfect, but it is something….. Go to User->User Commands->Edit User Commands. Then, in the text box supplied, insert (all in one line):

pdftotext -nopgbrk %.pdf|sh -c "wc %.txt > %.wc" |xmessage -nearmouse -file %.wc|rm %.txt|rm %.wc

Voila! This will count the words in the actual PDF file, that is, references included. It returns line count, word count and character count. Obviously you will need to generate the PDF before counting words.

It is very sad that there is no way of passing selected text to user commands to be able to count individual sections, but alas… this is better than nothing. Ahh… texmaker… you could be so great if you took plugins.