Rope caulk sounds like a great option but I've done a bit of Googling and got contradictory advice. We have windows that swing open horizontally on a central pivot. Will the caulk stay in place on the window frame if we open and close these windows frequently? The stuff I put on the door is a self-adhesive brush pile draught excluder strip and stays OK on the door frame but peeled off the window frame a bit. May be something to do with damp?
I'd like to have a go with caulk or similar before I go for double glazing film, I think, as it's the gaps round the edges that cause the most draughts and it seems less 'naughty'.
I am using a product called seal n peel (which is a caulk like substance) this winter for a few problematic areas (disused fireplaces), it is designed for the same purpose as rope caulk . . . which is to stay removable. The purpose of these items is to seal a drafty door or window for the season and then be removed, not to be repeatedly worked by opening and closing the door/window.
If you want to reduce drafts,but still be able to open and close the window I would suggest looking at your windows and determining if the weather stripping is worn out. It sounds like your wants align best with replacing or upgrading the weather stripping.
I am not sure how caulk seems less "naughty." Around here there are newer homes with double glazed fixed windows that will still do the film over the window for a little extra r-vaule and it is accepted, whereas if I were a landlord and saw that my tenants were applying caulk to my building (especially if I assumed it were permanent) or doing doing any other "improvements" without my permission I'd get concerned; concerned about their skills, their choice of materials, the possibility the would demand a rent credit for the work they had done, and so on. So, if you go the weatherstripping route you probably should talk to your landlord.
What is your relationship like with your landlord? I've had corporate landlord that would not address issues even when I told them what the problem was and how to fix it (with ~5 dollars) in parts, I've had individuals as landlords who would tell me to go ahead and fix things if the cost was reasonable and deduct it from the rent while submitting documentation, and my brother-in-law has a landlord now who want to install a pellet stove and asked if him and his wife would be interested in installing when she purchased it.
Depending on who pays for the utilities your landlord might be receptive to working with you to fix the issue.
