Nutrients don't go away because it's cold out. Water can help leech nutes, but water happens year round, it does not get worse or more leeching in winter.

Which kind of banana water are you making? There's a couple different versions.

At the risk of coming across as a Negative Nelly, while the DIY use of banana water has some popularity, there is no scientific substantiation that it does anything for your plants. Just soaking the peels in water releases almost none of any nutrients the peels might contain - they really need to be composted for that to happen. So the water made from soaking banana peels for a few days will add only infinitesimal amounts of any necessary plant nutrients and in no way can be effectively substituted for a proper fertilizer.

Also banana farming is pesticide intensive, with chlorpyrifos (an organophosphate) being the primary application. While the peel protects the banana pulp from pesticide contamination, the pesticide is easily transmitted to your banana water and it therefore cannot be considered an organic or natural fertilizer, even if it were to produce significantly more dissolved nutrients than it does.

You would be far better off actually composting the peels, which will release nutrients and also negate any effect of the pesticides.

btw, 'leEch' is a blood sucking worm: 'leAch' is the action of pulling materials from a substance by the use of water.

I've just been putting the peels in a jar of water and letting it sit overnight or a little loner than applying it to the base of the tomato plants;