A warm blanket is only warm because it keeps the heat in but a machine in a shed will get really cold and once it does the blanket will only change the rate at which it changes temperature.

Covering from leaks is obviously a no brainer but to keep it dry you need a source of heat, some people just put a light bulb inside the machine and cover. In that case the insulation would help.

Another option is something like boeshield which is a rust protection spray. Or maybe improve the shed or make a shed within the shed from foam?

Cheers,

Graham