Hmmm...
I was a little surprised to find recently that the required gear list for a British Columbia Cave Rescue training seminar in Canada included "2 cowstails, minimum 9mm dynamic rope, with 2
locking carabiners" (emphasis added). By contrast, I couldn't find any US National Cave Rescue Commission material that specifies one way or the other - so one must assume that personal preference prevails (and rightly so, in my humble opinion). I don't know if the NSS Vertical Section has an "official" recommendation on this, but it would be interesting to find out (anyone?).
Out of curiosity, I looked up this subject in my 3 major vertical caving references. Here's what I found -
On Rope (USA), 1996, page 133:
Drawing shows a locking carabiner on the long cowstail, and a non-locking one on the short. Text states "two D shaped carabiners. If intended use is other than simple rebelay negotiation, a locking carabiner may be preferred. Europeans prefer non-locking because they are fast and easy to operate." Also states that cowstails should use high-stretch rope of at least 10mm diameter. Drawing shows figure-8 knots at both ends and the middle of the double cowstail.
Vertical (Australia), 1988, page 10:
Photo clearly shows non-locking carabiners. Text does not mention anything about the carabiners being locking or non-locking, but does emphasize using at least 9mm dynamic rope for cowstails and checking/replacing the rope regularly. Photo shows figure-8 knots at both ends and the middle of the double cowstail.
Alpine Caving Techniques (France), 2002, page 41:
Again, drawings clearly show non-locking carabiners. Text states "each length (of cowstail rope) ends in a loop...into which you place a non-locking carabiner." It goes on to suggest the use of keylock carabiners, but interestingly it advises against using bent-gate versions. "Bent gate carabiners may appear to be more convenient...mainly because they have a larger opening. But in some cases - for example, sudden twisting on the rope, cowstails stiffened by dried mud, or a traverse with a sharp turn - a bent gate carabiner can actually be very dangerous. It can snap open under pressure from the rope, releasing the cowstail from the safety line." It also describes using 9-11mm dynamic rope, but states "we do not recommend using a figure-eight knot (on cowstails)...it is bulkier, will wear more quickly and takes longer to tighten down to it's final size." Instead they advise using simple overhand knots at both ends and the middle of the double cowstail.