Hmmmmm.....how do you know you have a problem with spider mites? These are not plants that are often plagued by mites. And webbing associated with mites is usually extremely fine and centered in the joints of stems or leaves - no real cobwebs, per se.

It does no good to treat the soil - mites live only on the foliage. Maintaining high humidity levels is generally enough to discourage them - they dislike damp, humid conditions and the hydrangea doesn't appreciate being kept too dry anyway. Hosing or spraying down the plant may be all that is necessary, otherwise a very thorough (as in under the leaves) treatment with Neem oil will help. As they are in the process (or are about to) of losing their leaves, you don't need to treat now, but should resume in the spring once foliage reappears.

Climbing hydrangeas are quite slow to establish to the point where they will flower - 5 years or more is not unusual - and moving them can extend that period longer.

Why don't you release ladybugs or similar enemies of spider mites? It is kind of late in the year for that although some stores may still have them in instore refrigerators. If none are available, wait until the beginning of Spring to release them.