Forget me nots are rampant self sowers and spreaders. If you want a garden filled with forget me nots, put 'em in the garden. If you want room in your garden for other plants, toss 'em in the compost.

You can transplant them now and they will come back to bloom in the spring. And self-seed. At which point, if you so choose, you will have even -more- compost.

But oh what lovely compost.

Springcherry

And if you don't transplant them, you'll still have more forget-me-nots in the spring than you know what to do with.

Thank you...yes, I know how rampant they are :) But I have empty, freshly tilled gardens. I will transplant the Fortget-me-Not, since you indicate they will overwinter. They are so easy to pull and discard as desired. They are lovely come spring. Thanks to all of you!

The seedling that germinate in the fall over winter green and leafy untill spring. The seeds germinate for me when the ground is still frozzen. I get clumps of fifty seedlings every spring in my pots ,as rodents like to collect them into small piles.

I enjoy how forgetmeknots have a way of self seeding and appearing in a pleasant surprise sort of a way. ANd I especially enjoy seeing creeks along the side of the road with the cheery blue flower sprays.

Forget-me-nots are the state flower of Alaska and they grow throughout the state, which means they survive temps of 60 or 70 degrees below zero. I don't think you have much to worry about in balmy Zone 6.

Forget-me-nots is a name that applies to different species of plants. The Alaska state flower is the genus Myosotis and isn't all that easy to grow from seed. It's the 'true blue' color of the Myosotis that's quite striking. I wouldn't think that this is what's sprouting from the window boxes.
Other native forget-me-nots are the genus Eritrichium and garden varieties can be other genera as well.

One would have to know what 'forget-me-not is actually sprouting in the window boxes.