I go by the manufacturer's service intervals in the manual. For my 2012 Grand Cherokee Summit, that is 8000 miles. (MY14 is 10K miles) I do use synthetic oil and have done so for many years.
I question the dealer stating that you should use the lower interval because of "cold and salt". Those are not normally listed as "rough use" things by the manufacturer. Heavy towing, substantial off-road use, taxi service, etc., generally shift things to the lower interval under manufacturer specifications. Your owner's manual will tell you what is considered "rough use" for your particular vehicle. In my experience, dealer service departments typically push for lower fluid change intervals because of...profit. We had one local dealer that pushed so hard on that point that we have never returned to them for that vehicle and just use a local independent shop for everything except warranty work.
--
The most expensive tool is the one you buy "cheaply" and often...