How can I hook up my hot and cold water clothes washer spigots to have one garden hose with warm water for use outside? I am having a charity dog wash in June and need warm water outside!

Sorry, just had this image of a doggie spinning around in the washing machine.

But you go to a hardare store, they sell a "Y" basically it hooks up to the hot and the cold connections and then goes into one.

I bought one at a appliance store before, you also can make one most likely out of one of the Y adapters

I agree with Chuck but can't give him a greenie just yet. A "Y" conncetor would be the easiest and cheapest route to follow.https://www.google.com/#q=garden+hose+y+connector+shut+off&hl=en&prmd=imvns&source=univ&tbm=shop&tbo=u&sa=X&ei=ThKYT6PSJoay8ASRrbmJBg&ved=0CH8QrQQ&bav=on.2,or.r_gc.r_pw.r_qf.,cf.osb&fp=848ab178c6c7ec2&biw=1272&bih=808 Most have shut offs for both sides so you turn on the spigots inside full on, then control the temp by throttling the sht offs on the Y

I looked at the pictures and they don't seem to be wide enough to fit on the spigot directly. I am assuming that I can remove the washer hoses from the washer itself and connect them to this connector?

Yes, disconnect the two hoses from the back of the washer after you close the supply valves. Screw the two hoses onto the Y and then run a single garden hose outside. These connections tend to drip and leak so put a bucket unedr and around the Y connector.

Its Called a y mixer hose http://www.acehardwareoutlet.com/productdetails.aspx?sku=998043815 I just got one to wash my donkeys with good luck all