Peas should be fine, quite cold tolerant. If they haven't been hardened off at all then they could be damaged by the wind, so you need to protect them from that, or harden off over the next week, then plant out. Meanwhile, feed with a general vegetable liquid feed a couple of times, as they will have used up all the nutrients in their compost by now.
What size pots are they in? I now sow mine in 4" sq pots, 5 seeds per pot. They have taken 3-4 weeks to be ready to plant out - I've done 2 lots, one more to go. I have supported them with bushy twigs (from laying the hedge - never had enough before) and that seems to give them some protection from cold and wind. I used to start my peas off in lengths of guttering, but now I find the pots easier to manage. That would be useless with large amounts though.
Here we don't plant the delicate things out until early June, as we sometimes get frost that late, but peas would be fine sown direct outside if you can keep the mice away. Maybe you should sow a second batch now, just in case the first lot don't thrive.
Good luck with them.