Sorry I don't know know the name of the plant (unless its a Hippeastrum in which case it could well send up an impressive flower shoot if its not damaged),but its best to remember that its always unadviseable to put houseplants outside in winter even on days that are apparently mild as it can get unexpectedly very cold as you have found. If nobody else answers the following is the best I can do:

If the bulb has been frost damaged there is very little you can do except keep your fingers crossed.. If it has grown some more leaves it looks as though you have got away with it. Keep it in the house, and don't over water it (more is not better) but just gently moist. Am I right that there are some new shoots coming up round the main bulb? If it does send up a long flower shoot let us know & we will advise what to do next.

Sue - there is a photo in the main gallery.

Thanks Paul - never thought of that. Just had a look and I don't know what it is for sure do you? Wondered about a Hiippeastrum but don't think so.

Yorks: Albuca bracteata (looked up 'pregnant onion plant'.) Does that help any more knowlegeable (than me) gardeners?

That's helpful -this is what Wikipedia says about.says about it.

https://en.wikipedia.org/wiki/Albuca_bracteata#Cultivation

As far as what you do now goes I would follow what I suggested until it begins to look happy again.
(Must confess I'd never have guessed that it is actually known as pregnant onion! I thought it was just your name for it. Ignorance is a terrible thing, lol...)

The plant that I know as Pregnant Onion is Ornithogalum caudatum, close kin to the Star of Bethlehem. Just looked at the photo, and that's what it is. If it is damaged inside, it will wall itself off from the damaged portions, as long as it isn't over watered. You may see some weird, papery "sores" appear on the surface as it grows new layers from the center, but as long as they aren't black and mushy, it will be alright.

Glad you knew for sure Tug. Also confirms that my general advice appears does apply in this case! Thankyou!. Sophie you can smile again!

Thankyou all so much my friends, I feel more positive now. I will keep you informed of her progress.