Grey on deep, cool skin tones (Deep Winter)

The answer

No. Grey sits well outside the Deep Winter palette. The nearest thing in the palette is #F2F2F0, ΔE 22.2 away, which is one of the four neutrals the season is built on. Under 12 reads as the same colour family; past 25 the two are visibly different colours.

It does not collide with anything on the season's avoid list, so the only question is distance.

How grey scores across all twelve seasons

Grey is an opinionated colour: Light Summer scores it 88 and True Spring scores it 32. A gap that wide means the colour genuinely decides something, and getting it right is worth the effort.

Deep Winter sits 9 of twelve at 45, 44 points behind Light Summer. That gap is the honest size of the compromise, not a verdict on the colour.

• Light Summer: 88 (ΔE 4.7).
• Soft Summer: 87 (ΔE 5.3).
• True Winter: 86 (ΔE 5.8).
• Deep Winter: 45 (ΔE 22.2) <- this season.
• True Spring: 32 (ΔE 19.9).

What to wear instead

Nearest first. These are the colours in the Deep Winter palette that get closest to what you wanted from grey, so the substitution costs the least.

• #F2F2F0: very light, a white (ΔE 2.0).
• #3E4148: deep, a charcoal (ΔE 3.3).
• #1E4A3E: deep, a forest green (ΔE 5.0).