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Done a few UK mountains in winter conditions.
First couple we had no proper winter gear... Turned back 100m ish from the top in both cases, on the first one (skiddaw) because no grip and massive winds meant we had to belly crawl across the hard packed icy dome of a summit and it was getting much more risky than it was worth, and on another (snowdon via the pyg track) because of a section where the path had a significant drop below and snow had drifted and been had packed so the path was actually a thin icy slope pointing straight at the drop below... Again, the risk / reward wan't favourable.
Third time however, I'd bought a couple pairs of crampons on ebay during the summer (about £25/30 each for grivel monte rosa with new classic binding, good shit IMO) and a couple ice axes. That shit made all the difference and we summited snowdon via the pyg track in snowier conditions than the pervious attempt, fuck yeah. Pic related is us at the bit we bailed on the pervious year.
So my advice to you would be to get crampons and an ice axe, and be prepared to turn back if needed. BRING A HEAD TORCH TOO. Layers. All the usual shit. Winter mountaineering here seems to be a little erratic (though I'm no expert) and can be lovely at the bottom of a mountain and deadly at the top, changing weather, bla bla bla.
Get a walking axe not a climbing one btw. Long straight shaft, use for stability in your uphill hand and as a brake if you take a slip (learn that shit, self arrest it's called but there's variations on teh theme). Same with crampons, flexible walking ones paired with sturdy boots. More shit to learn about.