I am currently endeavoring on an Antarctic expedition and wanted to know more about different repair options for our tents in down to -80 temperatures and in extreme high winds.
The best answer is to consult with the manufacturer, expedition grade tents are usually bomber proof but I respect that you always want to be prepared for the worst. My strategy:
Small punctures and tears: use a cold weather tape such as Echo All Weather Repair tape which can still form an adhesive bond in -30°C. Apply it to both sides of the tear. Don't bring the whole role, instead bring several metres rolled onto itself or wrapped around something that can easily placed within your coat to warm up if necessary.
Larger tears: Either bring a metre square piece of material set aside for repairs, probably the same material as the fly, or if weight is your primary concern have a strategy where you can repurpose something you've already got on hand such as the top portion of your bivvy sac, the cover of your sled, or a goretex shell. Cold weather tape could again be used to seal the edges and the rip, but you'll want a more permanent bonding agent that adheres in cold temperatures and remains flexible. Look for silicone glues which are rated to -30°C or lower.
Final thought: don't wait until a rip happens to discover whether your technique is viable, set aside some time at your staging camp to test out which techniques work best.