Indoor or outdoor ceremony In October?

Both areas are very beautiful. Do you live in a warmer state? I live in New York so I'd probably would go with inside because here it can get pretty chilly around that time and a lot more chances of rain. But if you live in a warm state I'd say have it outside and see if they can have the inside as a back up plan incase it's too hot, cold, or rainy. My cousin had his wedding outside at the end of August, it was cold and rainy and the place he had his wedding let him move the wedding inside and it was still really nice.

I'm so worried about weather that I always choose inside. How hot do you estimate it could be outside? Maybe from past temperature records

Both are beautiful. The inside doesn't need an arch with the existing decoration. Flowers go with anything.
Check almanac.com for weather predictions. Is October where you are normally hot or is it comfortable? I can't imagine it would be any different this year than in the past. It all boils down to personal preference.

Would you be able to plan for outside and have the ballroom as a contingency plan in case of weather? I'd go with outside so you can showcase your arch

I would do the inside if you’re worried about weather

If you go inside don’t use your flower arch it will take away from the natural beauty of the venue

Do you live in a warmer state because I live in Maryland and it normally isn't too hot to get married outside in October?

I'm a sucker for outdoor ceremonies, so that has my vote. Obviously, if it's going to be 100 degrees outside, may not be that great of an idea. You could always get some sort of tent to cover your seating area.