Jan, take a look at
www.autobandenmarkt.nl and go to shop and look for 305-40-22 tires..
You can find some summertires but i didn't see tires especially for the wintertime..
There is only one tire for all weather.. That's the GRABBER UHP 305/40 R22 114V XL
You can also click at "autobandentest"
There is also a Pirelli all weather tire but this tire is a littlebit higher 305-45-22
( i don't know if you can use those tires in combination with your lowering kit)
Go to 305-45-22 tires and look for the Pirelli Scorpion ATR tires (not cheap)
Maybe you can find a good tire for your truck on this website..
I can't tell you any experience about those tires because i found this info on this website..
Alex bought some weeks ago 4 new tires for his Nightrunner wheels from the same shop..
They ship the tires to your home and you must look in your neighbourhood for
a shop who can put the tires on the wheels and balance them.
I will use my truck as long there is no salt on the roads in Holland... The wintertime really sucks!!
