Your geirmination will take a long time and spotty if no water. If you are concerned with a swift rebound from the cold season then don't overseed with rye which will compete for water an nutrients beneath the soil.

I have done it twice without watering.
1) Core aerate
2) Pass north-south, then east-west with the seeder.
3) Wait for rain.

I don't think I'll bother this year. I had planned to do it with supplemental water this year but the ban has squashed that plan. You cannot aerate without the ground softened up first. It will not grow with out a few waterings and if the seed sits too long, the birds will eat it.