Hi Louise,
I’m in NJ zone 6 and started a herb garden two years ago. Last year we had a record amount of snow and some pretty prolong periods of cold.
For Rosemary - it’s frost hardy but wont like it much below -5’C / 23 ‘F.
I had some old plastic
milk crates which I put over my rosemary before heavy snow or harsh frost. I then covered with an old white bed sheet, so some light would still get through. The bed I grow it in is south facing. The plants remained buried for a month and all three survived. Snow can act as an insulator so may have kept the temperature high enough. I gave the plants a good autumn prune and used some of the sprigs as cuttings and grew on indoors in pots for insurance.
There’s a thread here on permies -
How to take Rosemary cuttings
For Thyme - it’s a tough plant. It will survive down to -15’C / 5’F easily. I have dozens and many different varieties and it thrives. I didn’t give it any protection. You can also propagate and here’s a thread you might find interesting:
https://permies.com/t/124338/Thyme-propagation-technique-mini-hedges
I’ve never grown zaatar - I cook with something called Za’atar which I sprinkle of pizza dough along with garlic and butter. It has Oregano in it, which I grow and didn’t protect. It’s amazingly vigorous and although it didn’t look great when the snow melted, there was a huge amount of new growth a month later.
My biggest concern would be the pots you are growing them in. All my plants are growing in the ground. On the plus side you can move them to make the most of heat from your house and early morning sun to warm them up. The
roots of a plant in a pot are going to get more temperature fluctuations than a plant in the ground. If they’re small enough then as mentioned a cloche might be a better option.
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