Contrary to common perception wood composite kayaks are stronger than fiberglass and plastic kayaks. The construction is sandwich. External layers (inside and outside) of fiberglass & epoxy with a wooden core in our constructions. OneOceanKayaks says a lot about the construction on their webpage "Composite Sandwich Core Panel - mechanics and principals". I wanted to add a video demonstration to convince sceptics that think pure plastic or fiberglass is less trouble. Find the video I am referring to lower down. My daughter is rocking the boat on the ground while I stand on the deck of the other end. No harm done.
A mended fiberglass boat is likely to require more skills to reach the original strength. A fiber boat with comparable weight to the wood composite is also likely to break sooner ie. more mending needed. Add the lesser risk of dropping or hurting yourself with handling a 5-10 kilo lighter boat.
If you plan to break and dump the broken kayak for the winter, then you should go for the plastic. Water and ice will not make you worse off for the spring when you want to fix that leaking crack. What you need is similar plastic and a substancial amount of heat to quickly melt some new plastic and bond it with the edges. Fiberglass and wood kind of rots when swamped with water, but the rot does not happen much faster with epoxy&fiberglass laminated wood than with fiberglass that has lost its protecting gelcoat. The styren resin used when building fiberglass boats soaks water when exposed, as opposed to epoxy that is water resistant in comparison. The wood also soaks water but only to a limited amount. And since air is blocked by the water few microbes will enter the exposed wooden parts of the core. The soaking is demonstrated in the video referred to in this article. I also had a laminated piece out in the snow over the winter, big parts of wood exposed in the cuts, and minimal harm seen. Sadly I burnt it some weeks ago and could not add it to this video.
Mending a wood composite kayak can require as little as adding some epoxy to the surface. In the worse case you would push back the wood sticks so they match, dry the wood and soak the area with epoxy. Then sand it and add a new coating of fiberglass and epoxy. Sand it again to the finnish you need, and it is as strong as it was. Optionally you might want to glue in some new wood with the same colors and then finding the old damage is guesswork.
Mending fiberglass boats is not really difficult but is likely to require a bigger patch and might need something to act as a mold. Small cracks in the gelcoat (the colored hard outer shell) need to be opended and cleaned. Start with one side. Make sure the structure stays until you have enough stiffness to avoid molding/modelling. You can use epoxy. In fact epoxy is gerenrally recommended for repairs. Once you have replaced the broken old fibers with intact fibers, and sufficient thickness, then space for the colored gelcoat is grinded by sanding. And then apply gelcoat, with some repeated sanding for a nice finish.
To have and to hold a dear kayak for years and generations it is better be enjoyable and inspiering by looks and performance. Invest in a wooden kayak.