Wind protection would be beneficial.

Here is my Natchez, even with burlap or row this is going to be hard to cover. I broke a couple canes trying to move them. I may tie them to the fence and cover fence. I have a fence and trellis here. Behind it are Columbia Star, Loch Ness, and Black Diamond covered in leaves.

I was scared. I think even the Boysenberry says it is hardy to Zone 6. And Zone 6 dips below 0 F several times each winter.

In general, TC should be ok with Z6. But Z5 can have damages. I think that was what happened to Drew....

I had boysenberries (thorny) planted in the ground and in protected pots last year and they are not hardy to zone 6a or 6b, according to the latest hardiness zone charts. Zone 7a, with a low end range of 5F would probably be the lowest you can go without getting bud and cane damage. The advantage for boysenberries is that since they are trailing, you can cover them effectively and protect them several zones lower.

The further the blackberry cane extends out of the ground, the less thermal benefit it will receive from the ground temperature, even if you cover it. Semi-erect (Chester and TC) and erect (Apache, Ouachita) varieties won't benefit from covering them other than the benefit from wind protection.

Didn't you mention that your temps fell below zone 6a minimums...(e.g.-10F)? The closer you can get your plants to the ground and seal in the ground temp, the better they will be. My TC's grow upwards 4+ ft before they start running (e.g trailing). At that distance from the ground, you can't retain the ground thermals.

The row cover only helps retain the thermal energy that is present. Once you break contact with the ground, you will generally get the air temps which are much lower. That's why the crown survives while the canes do not.

I'm trying cardboard under the row cover to reduce the impact of conductive heat loss. My theory is that because corrugated cardboard has air pockets, it will lessen the transfer of cold temps through the direct contact of the cane with the row cover. I feel more confident of my theory after a couple of glasses of wine.

The +13-prone Rubus ursinus, our local trailing native, the source of many flavorful hybrids, occurs on the west (warm) side of the Cascade Mountains, at lower elevations.

The canes do get harmful winter damage fairly often in Z6, in my experience, including killing them to the ground some winters. I bet burlap over the top right to the ground would be helpful even here, not just by reducing wind, but also by holding heat from the ground a bit for the canes.

Be sure to bait out voles (mice) if you create any kind of shelter. I've seen them girdled in bad snow winters.

Well just be careful I got them down some but lost one as it broke on me. It can be done. It didn't matter the plant has canes all over the place. The plant is worth the fuss, it produces some excellent berries.