I would trim off the blackened part to just above a leaf which is still green. You are letting nature do your pinching back. Hopefully it will all work out for you. Next year, hold back until ALL danger of frost is over before planting.

it is so hard to tell when "All danger of frost has past" these days with Climate Change. I mean we thought we were done with snow two weeks ago (and the weather the weekend before it was lovely) and yet there it was.
Ma Nature has gone all hormonal on us.

Looking up historical lows gives you a pretty good idea, despite climate change. For me its pretty easy, I just remember a few years ago when a bunch of kids were camping on my lawn and the temperature went down to 0C on a May 24th weekend.

Another mistake people seem to make is planning for planting out pre-started Dahlias versus when others plant out tubers with eyes. In-ground frost has already past, and if you consider it would likely take 6 weeks for a plant to emerge from the soil, you realize that they aren't likely to be subjected to air-frost prior to mid-june in my zone, later if the tubers went in on May 24 as is customary around here.

Cheers,
Russ