I've never tried that, but I have used a trick recommended by Roy Klehm: cut the peony in bud, when it first shows color. The flower will open fully in the house, without ants.

Hey, that's a terrific idea! I didn't know they'd open if you cut them that early. Cool! Thanks much.
Karen

Would that be cutting it down the middle or making a cross cut?

I think he means to just cut the peony stalk when the bloom is in bud, and it will open in the house without ants. Not to cut the bloom itself.

You can also stick an opened peony upside down in a bucket of water for say, maybe 15 minutes or so. Chases all the ants out and doesn't hurt the peony a bit.

Good suggestions.

The ants are apparently not hurting the plant (or the flowers), just gathering nectar to eat. They aerate the soil, too, so there's no point in chasing them out of the peony bed -- just off of any flowers that are going inside.