I can't answer that for other companies, but because we install CertainTeed products according to manufacturer specs, we confidently install them right up until Christmas (and have also installed some in January in the past), without a hitch. We have never had any issues with roofs that we have installed late Fall and Winter. CertainTeed tar lines seal with UV, not heat. UV is present year-round.
Believe me, we do not want you to call us because a shingle has blown off at a time when the temperature is super low or while there is ice or snow on your roof. We would not be installing them if blow-offs or other issues can potentially arise. We answer our calls. We don't want this call.
Eaves troughs. The only requirement for eaves trough installation is that there is no precipitation on date of installation. It is not favorable for the installer to work in extreme low temperatures because, well... try touching metal for hours in the cold. Self-explanatory. Otherwise, your gutters are good to go. At any time of year, we observe the weather and plan accordingly. If he (or she!) is showing up on a rainy day, be concerned. Until then, trust that your contractor or installer is confident in the install.