Reapply sunscreen every 2 hours in a gloomy day, necessary?

Hi, I live in Finland, here is always either cloudy or gloomy, uv index level is always below 2, I wonder if I need to reapply sunscreen every 2 hours in this case? What about sitting in the office with the window open? What about in the winter? Here it could easily get to minus 20 degree, does the coldness effect sunscreen make it less effective? I am using Tizo 3 spf 40, its really hard for me to wash my hands every 2 hours just to apply the sunscreen.

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