I have some large Mex oregano that looked very stressed. They grow on a hill under some cedars on limestone marl. The recent rain has breathed life back into them with a million new leaves bursting from bare branches. Their old foliage was all dead. This plant is very tough and will rebound from extreme tryout. It is a xeric plant that will shut down and re awaken. I would say that it could take a good hard cutting back. I would think that cutting it back by a third would be safe. How large is your plant. My plants are 3'tall and wider. One is over 15 years old. They also grow from cuttings.

I cut mine back to about 6" every winter (December/ January) to encourage fuller form. They never fail to bounce back and bush out by April. I've even cut a few to a 1" stump when they've gotten to rangey. Still no problems. Hardy little buggers.

Mine is at least 10 years old and is about 3 feet tall and pretty wide. It put out so many leaves with the May rains, then suffered all summer. Now it's mostly naked wood with very few new leaves coming out. I'll trim it pretty hard and see what happens come spring.

What is the coldest temp that your plants have survived?

13Fback in 2010 and they are still vibrant. Mine were in dry limestone ruble and some compost stuff on top. They had good drainage. I do not know what they would do in cold damp clay at that temperature.

It got down to about 17 at my house one winter and stayed there for several days. It made it just fine.