I'd highly recommend Schwalbe Nobby Nic / Racing Ralph combos.
Newer Schwalbe tyres are the correct size these days, so measure rear clearance properly! They're also better constructed, which means sliiightly heavier but much better grip as the tread stays in its pattern better.
I've used this combination in 2.35/2.2 but with RR front NN rear in the snow before (trails and tarmac, nothing too gnarly) and on icy roads & found it to be totally solid. Also used RR 2.4's front & rear, same conditions and no slippage (and this includes riding up hills down hills, 90 degree corners, pavement-hops, etc - such a fun way to get to work when there's no cars on the roads!) If you get Schwalbe Trailstar (slightly softer) compound they are exceptional, just up the pressures when it's dry for good rolling resistance and drop when off road/it snows/ices up.
Sammy Slicks are exceptional '3-season' commuter/gravel tyres, but no way would I trust my life to them in snow. The knobbles don't wear out on tarmac when the pressures are set right (high), but any semi-slick with edge knobs will by its nature snap more suddenly than a rounder tyre when it loses grip - this is why Ralphs work well as they're rounded and Nics in the softer compound grip exceptionally well if you keep upright and if you lean they lean downward through the square edges more. Ralphs will slide sideways when it's icy, but won't snap out. Nics seem to dig down better into the snow/mud/etc.
The older Schwalbes were very thin, and they still make these (the lightest weight constructions) but these do get damaged and torn easily. Anything under 500g per tyre is likely to be this very thin carcass and give no puncture/damage resistance (you can literally stab through the tyre with a Biro!).
Most of the 2.2"-2.4" tyres are 530-580g for folding bead, which is very reasonable.
Rocket Rons are fine if it's dry, but clag up at the first sign of dirt, leaving you with a slick.
I'm assuming you can't fit 2.5" tyres...? That's another bundle of soft-compound fun in the snow & ice