In general, seedlings can't be planted in the ground until approximately June 6th. I can put them out earlier depending on the long range weather forecast. There is generally a cold snap that hits mid to late May. It lasts 2 days and after that the coast is clear.
I start to harden the seedlings by bringing them out on above freezing days. The optimal days are cloudy to allow the seedlings to adjust to natural light. I bring them out the first few days for only an hour. Then I increase the outdoor exposure time an hour every couple of days. I keep them out of direct sunlight for a couple of weeks. They are brought in every night for the first couple of weeks because there is potential for high winds here in May. I use a piece of insulation board as a wind break.
It takes time to transfer 60 flats in/out every day for a month. But it is worth it. By planting time, the seedlings are adjusted and ready for the ground.
Example of local weather in mid May see this post in 2013: 25F (-3.8C) Last Night - Covered My Precious Hops And Peonies - 05-14-2013
Or this post about May 17, 2016: http://backyardorganicgardener.blogspot.com/2016/12/snow-flurries-on-5172016-and-status-of.html
And planting time-to-plant rules I follow: When Do I Plant