For primary protection against the wind, a clear acrylic sheet fastened to the outside wall & sealed with decorator's caulk - this is not great outdoors long-term, but might be easier to get off in spring than regular outdoor mastic or silicone sealant.
Acrylic sheet will actually deform in the wind, so if you seal the edges completely, it may cause further compression against the glass. It might be wise to leave a little breathing room by not completely sealing the bottom edge.
For secondary protection - & also has some heat-retention properties - UV window film Random Amazon search. Applied to the inside it will add some safety if the window does actually fail, like a poor-man's laminated glass substitute.
It is removable, so if all survives the winter, you could add a bit of sun protection there or elsewhere in the house for summer.
After other answers - I didn't realise you could get shatterproof film for a similar price to UV/mirror film, I'd assumed it would be far more expensive. The difference is thickness, strength & tear resistance. If you can get shatterproof in budget, get that instead.
Fitter's note:
This stuff is awkward to work with. Though it has no adhesive as such, it will cling to itself as you try to install it, more than you could imagine possible - think of handling a 6ft square of cling-film/saran wrap, then imagine if it is actually sticky too… and also covered in soapy water. Anything larger than maybe 3ft square is a two-man job.