Long-form storage is inherently unprofitable - a battery that's used daily will make 365x the sales of a battery that's used only once a year.
So inevitably, the first batteries will always prioritize daily arbitrage, and only once that market is capped out will some battery projects target weekly/monthly/yearly arbitrage.
In countries with cold winters, the obvious solution is heat-energy storage systems, which don't output electricity but instead store and output heat directly; they're basically just a big pile of sand/stones/bricks wrapped in a ton of insulation. Thanks to the cube-square law, they scale up unbelievably well and can easily store months worth of heat.
Due to that scale they don't make much sense without district heating, but energy storage is a numbers-game and lots of cold places already have district heating that could be quite easily retrofitted.