>>2857805>>2857834in your position it will be difficult to find lightweight insulated boots for chasing down illegals.
First things i'd consider:
1) Wear wool socks. Preferably 80% wool but at least 70%. I use Darn Tough for warranty but they are too restrictive overall. Costco usually sells wool socks during winter. Prob best value.
2) Switch out to a wool or heat reflective insoles. Something like this.
https://www.amazon.com/gp/product/B00DWSX3TW/ref=ox_sc_act_title_1?smid=A3SJX7TTM3PAEZ&th=1&psc=1There's also thicker wool felt insoles from Canada on Amazon but they tend to take too much volume w/o sizing up.
3) Make sure you're not overtightening. A lot of your veins are on the top of your foot so over snugging your shoes/boots will cut off some of the circulation. Even too tight of socks will do this. If your boot fit is too tight from socks, lacing, undersizing, pushing your toes in, you may need to go up a size. Sadly some of the suggestions above require going up a half or whole size. At the end of a shift your foot can also swell up half a size. Also as I mentioned with toes, your big toe in particular, if it is pushed in part of its circulation is cut off. Even though I wouldn't use them for work I found toe spreaders helped fix the circulation issues in my foot.
4) If your socks wet out from sweat/melted snow, change socks throughout day.
5) More $$$ but you can buy heat packs you can put in your shoes.
The most popular cold weather boots you'll find in like Alaska are gonna be boots like Mucks that use Neoprene as the liner and above the ankle and polyurethane (looks like rubber) at the foot). Like picrel but you're looking at like 6 pounds per pair.
If I tried to make the perfect shoe/boot that was light i'd probably go up an entire size on a wide shoe/trail runner and use wool socks with a loose neoprene outer sock to keep it warm and water proof without relying on dogshit goretex but that would take a lot of experimentation on models/sizing.