Okay, this is how I dye yarn or knitted woollies.
The same would apply to wool wraps, but I wouldn't like to say how the heat/vinegar would affect the elastic or fastenings
You can use either food colouring (with vinegar to set the colour) or koolaid (which has citric acid in to set the colour).
1. you need to soak the wool until it is wet through (colour will only be absorbed in the wet bits so it needs to be evenly wet).
2. Mix up whatever you are using with water - and vinegar if necessary - and add to a bigger bowl of water. The amount of water doesn't matter (as long as there is enough to completely colour the item) but the more food colouring or koolaid, the stronger the colour
3.Put your cover in it and swish it round so the dye goes all over it, the more you swish the more even it should be (although you are unlikely to get a completely 'solid' colour).
4. Then you need to fix the dye with heat - either in a microwave for 2mins at a time cooling in between, or put the bowl over a steamer and heat like that. When the water is clear the dye has all been absorbed and you are done
5. Rinse and lanolise!
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