First, when it gets to -3°, most of us say screw it, no need to pick up a wrench.
In general, you're asking for too much out of a single pair of gloves unless you want to spend
a lot of money. I have mitts that are good to -50° but no good for working with tools. They are made to have another pair of gloves underneath and you peal them off if you need to do anything.
IMHO, your best bet is to stuff your pockets with a variety of gloves. I use simple cotton gloves if I don't have to touch anything until it gets down to about 20°. After that, it's pull out some North Face for insulation/warmth but they're no good for working. For working, I switch to something like you linked to. I then switch back and forth based on what I'm doing. Once you get started, stuff the gloves inside your coat, under your arms instead of putting them back in the pocket. They're warm when you pull them out. No matter what, if moisture reaches your hand, DO NOT put those gloves back on.
It hasn't been cold enough to pull out the winter gear yet but I'll keep my eyes on my favorites.