When it comes to winter riding in moisture, natural ropes will become a little more stiff. Use an old one that flops the rest of the time and save your newer firm mecates for spring through fall. DO NOT use man made fiber ropes on rawhide or leather bosals. They can permanently damage the bosal.
A mecate without a core may be soft in the rider's hands, but it is not going to last. The feel of the rope will not maintain. The heart of the mecate is the core. Those built without cores are very cheaply made.

The prickly hair will wear off with use. If needed, try light gloves. Do NOT cut, burn or sand paper mecates in an effort to remove the hairs. They are integral to the rope and these tactics impede the break in time and the usefulness of the rope.
Make certain that you invest in properly made mecates with plenty of protein rich fiber that are sufficiently twisted. Some fibers are known for stretching, particularly the curly/wavy yak. When sweated or damp, the results can be "interesting" especially used for a cincha. Although a creative use of the animal's soft hair, the yak was not part of the traditional CA vaquero cattle culture.