I agree you can't shorten the cold but you can feel a hell of a lot better using medications- I used to hate colds and now find that with only one/two day of mild aches and pains, I am usually ok. No need to suffer too much any more.
The best thing ever is xylometazoline which is a nasal decongestant, you squirt it up your nose- it's Otrivine or other cheaper brands. This works for hours, you can sleep without that awful blocked feeling. I no longer dread getting colds now since I discovered this stuff (not on commission honest!)
Then- you can take, if very achey, paracetemol and ibuprofen together (or rather look at the max doses and then divide them up through the day)- these are not incompatible with each other.
For the red nose (after the Otrivine) put Sudocream on overnight (cos you can breathe due to the Otrivine) and it won't be red and flakey- also works for spots before the big day.
Use medicated/soft tissues, eat pastilles/throat lozenges- if you need to speak in public (at the wedding) then use Proctor's pastilles as they are tiny but very strong so you can keep one in the side of your mouth and still speak.
I also take echinacea and lots of vits anyway in winter, and wash my hands like crazy.
This might sound a bit OTT but I dreaded every winter due to getting every bug going, now I realise you don't have to suffer that much if you get the right medications and can sleep well.