Attrition accumulates per day, according to a base value added to a temperature/humidity factor. The next day, the base value is the previous day's final value, which is then added to the current day's temp/humidity factor. Rinse, repeat. Here's another way of looking at it:
Attrition(0) = Base damage + Climate factor
Attrition(i) = Attrition(i-1) + Climate Factor
Now the whole concept has been simplified to a single factor, that is temperature and humidity. Those two variables, also called the heat index, should cover the vast majority of the effects of weather on the human body. Precipitation will be factored indirectly, namely, heavy rainfall washes out (or covers with snow) paths and roads, which lengthens travel time, allowing for more attrition to take place.
Now here we are at a crossroads, what numbers do we use? D&D was built on pulling numbers out of assholes in order to answer this question. This is where your design fails too, you do not have to guess at any of these numbers at all. Thanks to the information age, you can find peer-reviewed research on pretty much any topic you want. There is no reason to be building systems out of fairy tale numbers of useless heuristics you just made up.
Ok, so where do we find this information? A quick google search lands me at the Center for International Earth Science Information Network, and a handy research article called "Climate Effects On Human Health". Why, there is even a section of predictive equations! Who would have thought of this, there already IS a system for determining how your environment affects you. All we have to do is translate it into hit points and we are off to the races.
So stop pulling numbers out of your ass for your designs and put in the same amount of time into basic research.
Ok ok, back to this system. Let's see what we can use: TMR = cycle + 0.10e[0.2(F - 90)] This looks extremely similar to what I want, a "temperature-specific mortality ratio" expressed as a base value added to a function of temperature. But I want heat index, or a value that combines temperature AND humidity. Thank you NOAA:
We have all of our pieces now. Stick our predictive equation into a spreadsheet along with inputs for temperature and humidity. Input the above chart into the spreadsheet and perform a look-up to pull a heat index value to stick into the predictive equation. Then, tune the factors around the exponential term in the equation as well as the output so it translates into usable hit point numbers (nothing too small or too big).
Once the sheet is set up, it takes less than 1 minute to generate an attrition value for the day's adventuring or travel. In the end, you have a system that gives you an answer as fast as you can open a spreadsheet and the answer is based on our shared reality and science.
Oh, need to find climate data for input? You have a few resources from which to work.