Space has no temperature
You could say space was at absolute zero - indeed an object sitting in the shade in space would be approaching that temperature. However, space is also very hot. Because there is no matter in space at all, the only way to vent heat is via radiation - on earth we can use air cooling to lose heat. An object in direct sunlight in space can reach hundreds of degrees very quickly.
There is two reasons that the telescope has to be at 0K. The first will be heat generation - digital sensors turned on for the long periods of time that these will be heat up, and heat means noise. By keeping them cooled near 0K, any heat generation can easily be taken away from the sensors and electronics.
The second issue is not dependant on the temperature that the optics etc are at - they could probably be at any temperature between 0K and 300K - but that, if left alone and unprotected, they would cycle between almost 0K and hundreds of K regularily. The heating and cooling would destroy any glass or electronics very, very quickly. By keeping everything at absolute zero, there is no heat cycle.
I don't know if I've covered all the reasons, and without a source and more information I may be wrong on some points, but there is certainly a lot of factors that have to be considered in space cooling that are just not issues on earth - with limited supplies of gas etc, you can't simply energise particles and vent them, and there is nothing to exchange heat with.