I'm not really a winter gardener so no definitive answer for you, but why not give it a try? All you will be out if it doesn't work is the effort and few seeds. I would think you'd have much better luck in the peas reaching a harvest if you provided a somewhat protected growing environment - cold frame, hoophouse, cloche, etc.

Not many of the local winter gardening sites refer to peas, even though they are a cool season crop, but nothing ventured, nothing gained :-)

FWIW, peas are often planted in sequential crops a few weeks apart in order to extend their relatively short harvest season. I'd start the seeds indoors in peat pots, harden them off a bit once they develop true leaves and then plant in a cold frame or other protected growing situation. Good luck!

Here is a link that might be useful: winter veg gardening in the PNW

I'm in SW Washington. I planted peas on July 6, 2009 and harvested until late November. Your climate is hotter. I would try planting every couple of weeks through July and August, and see what happens.