You can get blown in insualtion without demoing the plaster we did it in our 1905 house that was all plaster walls . Are the windows at least double paned since old windows were not and need to be replaced or at least have storm windows installed in the winter . But really new windows are just better always .

Best bang for your money is super insulate the attic. Next is storm windows. Blown in cellulose is awesome. Sorry but i hate replacement windows in old houses. I own three houses on the Maine coast. One has thirty year old vinyl windows that are brittle with fogged glass. The other has thirty year old wood windows with dry rotted frames and sills. All bound for the landfill. The third has storm windows over 120 year old windows in 175 year old frames. They are all in great shape, need putty and paint.

I second storm windows. 1840 original windows in my old place holding up better than 15 year old replacements in the same building. Our historic commission prefers originals plus storms.

Here's the reason why insulating older lath & plaster homes can be problematic: That era of plaster would also likely be balloon framed and have only wood clapboards or 1x sheathing on the exterior. That construction method is very air leaky, meaning air is moving through the walls from in and out and from low to high and mitigating any moisture (that is it's success). If you only add blow-in insulation into walls, or even tear out the plaster and add fiberglass batts with new drywall on walls, without addressing the air leakage from the balloon framing or the exterior envelope skin, could lead to the moisture causing problems.

Spray foam is an alternative, but would require removal of the plaster and detailing considering the sheathing/lack of and balloon framing.

Thick curtains do a great job of insulating windows.

I have an 100 year old house and, with the exception of one, they are all original with storm windows. The storm windows vary in quality, but the one replacement window is definitely worse than the original windows with good storms and not that much better than the ones with poorly-fitting storm windows. You need to redo the putty every now and then, but it's an easy enough DIY job. Our local dump has a huge pile of discarded windows, most of which look like they are not much more than 20 years old.

This Old House recommends sealing leaks in your attic, they suggest doing it room by room, you make a map of the elements in the ceiling below and use the map to find them in the attic subfloor.