From the research I've been reading (relevant to sports and also pain management), the 'cold' muscles people talk about is about the level that you and I are in when we walk around the house. If we go dance vigorously without getting the heart rate up we're quite likely to 'strain' something.
If we're intending to extend our ROM - yes it's the tendons, ligaments and other connective tissues that do the majority of the lengthening, but it's also the slight breakdown of the muscle tissue that occurs that builds muscle fibre and strength. To have good ROM we need both length and strength in the muscle unit (for want of writing the whole phrase out!). And if we try to do this without increasing the heart rate and consequent oxygenated blood flow, then we do risk strain. Pilates and yoga and other stretching regimes work best if your CV level is a little raised.
On another level, doing a bit of whole body jigging about also increases neural connections from brain to body to improve coordination before you start dancing...
I could list a whole lot of literature, but I'm not feeling particularly academic tonight. What I wanted to rant about was the DVD's that go straight into long ROM stretches without a murmer about needing to jog about a bit and get the big muscles active.
ah well, here's a couple of articles for the keen...
Warm-Up and Stretching in the Prevention of Muscular Injury
Authors: Woods, Krista1; Bishop, Phillip1; Jones, Eric1
Sports Medicine, Volume 37, Number 12, 2007 , pp. 1089-1099(11)
This is a link:
stretching exercises | stretching injuries | stretching warm up
Basically the evidence does not support stretching before exercise as a way to prevent injury in runners or dancers, but it does have some evidence to support it after exercise. Instead, it's suggested you do some basic CV warmup, do a bit of loose stretching to improve coordination and 'connection' - then go dance! Cool down properly with a good stretch and you'll be fine.