So I ended up buying a shower curtain like some of you suggested. I might still use the table cloth to add another "bubble of air" to the windows. I'm glad that the YouTube video for that window sealing kit put me up to this idea, because I really hate having things lying around that I bought uselessly and can't return... Will post pictures as soon as I get round to hanging that curtain, I think it should do the job nicely!
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For a shower curtain? Let me know how it goes!
Maybe there are grommets that work with plastic?
Just look for a curtain eyelet/grommet set. You'll probably get 2 sides you need to clamp together/hit with wooden mallet to get them in and the inside material should just come out.
If you want to keep drafts out, I would suggest tape! They make tape for putting up plastic storm windows that would also work well on vinyl sheeting.
Thanks, could you explain more? You mean I should put tape over the crevices of the windows? Because then I'd have to replace it each time I want to open the window, right? However, there's also a cold draft that comes from even the most well-sealed windows, because a sheet of glass just doesn't isolate as well as a wall. I guess that's what the curtain is supposed to mitigate.
I also have single pane windows that are drafty in the winter, and curtains just aren't enough, as the draft moves around it.
You can use the plastic as a second bubble of insulation by trapping an air layer between it and the window. You simply tape the plastic to the window frame, all the way around, and the trapped air bubble with help equalize any draft that comes through.
You can get kits for this that can be more easily removed if you actually want to open the window, but I had assumed that if you're trying to keep the heat in, you're going to be sealing the window until spring.
Here's a video showing the method I'm describing: https://www.youtube.com/watch?v=qQ2zinfyxQU
Thanks, that's interesting! Haven't seen that method before. I do wanna be able to open the window to let fresh air in, but it could be an option to seal off each wing separately... 🤔
You could also try to find clips like these, but I'm not sure how sturdy your plastic tablecloth is.

There should not be any drafts from well-sealed windows. Sure if the window is single-paned and it's really cold out, it will radiate cool. But a draft is moving air.
Well that is correct, sorry for getting the wording wrong!
You can buy something called sheers. Basically see-through fabric curtains.
They will look much nicer than a plastic table cloth, and will have the necessary bits to hang them with ready made.
You can buy (semi)transparent or translucent shower curtains that already have eyelets in them - at least round my way.
I'd definitely reinforce the holes, Especially if it will be moving around, or getting tugged open / closed regularly.
Maybe fold over a hem and glue it, or tape wrapped round the edge on both sides wherever a hole will be. Ideally you’d have metal or plastic eyelets in plane with the curtain, that the rings then pass through.
If you don't have a hole punch big enough for the eyelets then you might be able to use the eyelets themselves to cut their own holes. Assuming they’re two part metal thingd. put them in place on both sides and apply a clamp or two at the edges of the rings, gradually tighten and see if the rings are sharp enough to cut though, without getting too crushed . if not you could run a scalpel round inside the eyelet.
Of course any glue, tape, cutting method should be tested on some scrap material.
Melting through with a hot poker / soldering iron (even a cigarette) is another possibility, but might be hard to control, and messy / toxic fumes to consider, again a clamped on metal eyelet might set a boundary to the melt.
As much as you want to use this as a curtain, have you entertained a shower curtain that has the "grommeting" you need?
Alternately just put duck/duct tape along an edge and shove a sharp item through it to make holes?