Michelle, I have never done this before, but I'm going to take a crack at it for you.
Scarf number 1, in purple: the background color of this seems to be a very light grey, or perhaps a grey-lavender color. The print is large and very swirly. It has a bright purple, two shades of green (both cool-toned greens), and some black and grey. The purple is the main color. You could definitely wear this in the winter, and it is a very cool-toned scarf overall.
Scarf number 1, in green: This is the same pattern as the purple scarf, with the following color changes: the purple is replaced by a color that they call green, but looks on my screen to be more of a yellow/yellow-green/citron color. The greens in the first scarf are replaced by a magenta/berry color. This is definitely a warmer-toned scarf.
Scarf 2 is a black and white houndstooth. A houndstooth pattern looks like a check from far away. Closer up, you realize it isn't exactly a check--it is actually a "broken check" and looks kind of like a check on a diagonal. But it looks very much like a check. The scarf is pretty much equally black and white (the colors alternate in the pattern), with the border being black. There is also a little bit of grey mixed throughout.
Scarf 3 has a little bit of houndstooth in the pattern, but is not an all-over houndstooth the way scarf 2 is. It is more of an abstract patterns, with various patterns mixed into the scarf, if that makes sense. Houndstooth appears in various sections throughout the scarf, as does a floral print, and a print that is kind of made of small dots. The purple one has a combination of bright purple, lavender, dark purple/blue, grey and cream. The green has shades of seafoam green, teal, taupe and cream, and the blue has shades of aqua, darker blue (not quite ink blue, but almost), grey and black. The colors are mixed throughout all of the different patterns, so it all works together. I realize that from my description it sounds very busy, but it actually works together nicely. In each of the color combinations, the colors work together so that when you are looking at the scarf, the dominant color is clearly purple, blue or green (depending on which scarf you are looking at). I think that all three of these scarves are more cool-toned than warm-toned.