How Much Irrigation In Off Season

I've recently read about cover crops which as it was explained by the author he uses them in the off season mostly. I'm hoping along with other cover crops I can add some winter wheat (I've always wanted to grow and make my own bread!). He names this along with a couple other grains as a form of cover crop but that they don't fix nitrogen so to use them minimally.

Can someone give me an idea how much if any irrigation should be used for crops that are grown primarily to serve as cover crops? Water isn't really an issue because I will be harvesting quite a bit so if it increases yield or the overall productivity of the farm system, I'd like to use as much as needed. I just need to plan for its use.

Please advise

Brandon where are you located?
How much moisture do you get in the winter? Snow and rain?

I'm near Dallas. According to the data I found, our averages in November, December, January and February are 4.61, 3.62, 2.38, 3.3 inches of rain respectively.

From what I've read here and other places, we need 1 inch of rain per week. Would the rain requirements be the same 1 inch per week or perhaps just a percentage of this requirement? I know there are a lot of variables to consider, I'm just hoping to get estimated requirements to help plan for water harvesting purposes.