We are travelling to Mutianyu in october, is it high season?

It depends. In the early October, it happens to be the National Day Holiday of China lasting 7 days, so it would be crowded. In the late October, it would be not crowed that much. Thus you can go for a visit then. Generally speaking, people on Mutianyu are less than on Badaling Great Wall.
During October, the mild temeprature is good for traveling in Beijing. The average temperature could be about 15-16 C. Long-sleeved shirt and light coat can be appropriate.