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Holt-Winters carries three states: level, trend and a seasonal index per period. The multiplicative forecast is (level + h x trend) multiplied by the seasonal factor for the target period, so seasonal swings scale with the level — the right assumption when December is 15 percent above trend rather than a fixed number of units above it.
Multiplicative Holt-Winters
F(t+h) = (L(t) + h x T(t)) x S(t+h-m)
Multiplicative when the seasonal swing grows with the level, which is typical of sales. Additive when the swing is a roughly constant amount, common in temperature or headcount series.
The trend term is extrapolated linearly, so errors compound with h. Damped-trend variants multiply the trend by a factor below one per step and forecast much more conservatively.