Material of a winter rod
A winter rod has two different parts with two different jobs: the tip is responsible for sensitivity, the handle for keeping the tackle from slipping out of a wet glove.
Carbon
Carbon fibre. The most sensitive and lightest of the four: the hand's movement reaches the lure almost without delay. Stiffness ranges from soft to nearly rigid. The price paid for this is cost and brittleness: a carbon tip snaps from an impact where a glass-fibre one would just flex.
Glass fibre
Fibreglass. Heavier than carbon and usually stiffer, but it doesn't mind an impact against the ice and survives being carried in a box together with an auger. Sensitivity is lower, and a light touch has to be read off the spring bobber rather than felt in the hand.
Composite
Carbon and glass fibre combined in one tip. Middling in price and in sensitivity, with a good margin of strength — it's a compromise, not a separate property. Manufacturers rarely state the carbon share, so two tips labelled "composite" can differ from each other more than a composite differs from glass fibre. Most everyday winter rods are made this way.
Plastic
The cheapest and least sensitive. Stiffness is low, the hand's movement arrives with a delay, but a tip like this is hard to break. It's found mostly on the simplest constructions, where sensitivity is already carried by the spring bobber anyway, and on kids' tackle that nobody minds losing down a hole along with the fish.
Handle material
Cork, neoprene, foam and wood. The first two are soft and warm to the touch, foam adds buoyancy on top of that — a rod dropped down the hole won't sink — while wood is heavier and colder but doesn't dent. On the bare-winder rod the handle also doubles as the line winder, so there the material is also chosen for whether it holds the wound line and whether a sharp edge of the handle will cut it when a wet coil pulls tight.
What material decides in the frost
Two things you can't see in the shop. First: a cold handle pulls heat out of the hand, and the day on the ice ends sooner. Second: a wet, frozen coating stops gripping in a glove, and the tackle starts slipping exactly when a fish has taken it. Neither property shows over the counter, and both show up by the third hour on the ice.
Material is chosen for the load, not the price
Brands and exact compositions add nothing here. Carbon wins on sensitivity where the tackle stays in the hand all day, and loses to glass fibre where it gets carried in a box and dropped on the ice. So the tip's material is decided not by price but by how the tackle lives between fishing trips: one gets carried once a season, another every Saturday through a car trunk and a tent.