I don't often write replies; however, I do read the forum routinely. I couldn't let the topic of having your dust collector inside or outside your shop, slid by.
I build a new shop a couple of years ago and the shop is slip in to a heated/cooled work area and the other part is just heated storage area (North Dakota, you want heat). My plan was to place the cyclone dust collector in the heated side and pull the dust from the heated/cooled work area via the duct work into the just heated side. The plan was to reduce the noise factor.
Two problems, the dust collector pulled all my cool air from the work area and I couldn't open the door from my work area to the just heated side where the dust collector is due the vacuum that the cyclone dust collector had pulled. So, I had to add air return from the dust collector closet back into the main work area, so I could open the door (good thing I had a remote on/off switch or I may still be stuck in my shop, not all bad).
Having the dust collector on the other side of an insulated wall did reduce the noise some but the air return openings limited the effectiveness of the noise reduction.