Mark said:

I have raised 4 artichoke plants to a size about 2 to 3 feet across,
from leaf tip to leaf tip. This was a strain that had the possibility
of maturing in one long growing season, or taking the standard 2 years
to grow mature enough to bear fruit.

Here's my question: The winters here (zone 6) rarely get below 0
degrees (F)... Lots of winters, the temp never dips below the low 20s
or high teens. I hope (fingers crossed) that these temps are "high"
enough so these plants will survive and go on to mature next year.

In order to winter them over, should I cut them back before I lay
on a thick cover of straw, or should I just cover them as is, leaves
and all?

All I can tell you is to not get your hopes up. I grew artichokes from seed
twice. The #1 tip for getting artichokes the first year is to start the seeds
*very* early and get the plants outside to experience some light frosts.
This process will 'vernalize' the plants (make them think they overwintered).

As for keeping them overwinter in a zone 6 garden, it didn't happen here
(mulched with leaves) either time. The artichokes I harvested were much
superior in flavor to those available in the store, but smaller.

I think your best bet would be to build a cover over them (like a large cold
frame or small hoop house). Then you would have to watch for the soil
drying out under the cover. And you might have to start opening it as
the sunshine increases in potency in late February.

--
Pat in Plymouth MI ('someplace.net' is comcast)

Any technology distinguishable from magic is insufficiently advanced.
(attributed to Don Marti)