Why is there no cold water coming out of my shower head

I agree with Kelvin above regarding the frozen pipes. If the pipes aren't the problem and you have a thermostatic shower, then the problem could be a seized up thermostatic cartridge. Calcium build up inside the cartridge will stop the moving parts inside. It may be that the cartridge has seized up in a hot position, which won't let through any cold water, only hot.

Try taking the cartridge out and soaking in a calcium remover or vinegar. If that doesn't fix the problem a new cartridge is needed. (assuming the problem isn't the frozen pipes). Shower Thermostatic Cartridge Spares

If you live some where that gets cold one of your pipes could have frozen. if you can get to the crawl space/basement put a heater down there for a few hours and leave the shower cold water on if the water comes out of the shower your pipes have thowed out. here is a video https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0CDMQtwIwBGoVChMIn6q266OQyQIVAs9jCh3O6QFj&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DPbnGn9EG1mw&usg=AFQjCNEMOGXppMYQl-Rcij9L-P36CdC8Rw&bvm=bv.107467506,d.cGc good luck