First and foremost: I find this a very nice and readable solution. Good job!

All right, here are my two cents:

• There does not seem to be a reason for using Enum.map and Enum.filter on lines 7 and 8 respectively. I think it is nicer to keep your Stream a Stream for as long as possible.
• Maybe your function Weather.print might rather be named Weather.print_day_with_lowest_temperature_spread, although that would again be a very long name… In any case, print is a name that is not self-documenting.
• Although documentation is not necessarily part of the Kata, because documentation is a first-class citizen in Elixir, I think it is a good practice to simply always document your public functions in one or two sentences.
• There exists the function Enum.min_by/2, which you could use to clean up line 9 (Enum.reduce( &row_with_smaller_temperature_spread/2 )). That could become something like Enum.min_by(&temperature_spread_of_row/1) defp temperature_spread_of_row([_, max, min), do: max - min
• Nice job on outlining the functions in the pipeline. That is very readable .
• There is no check on columns that have the wrong data format. That is to say, you check if the first column in the row is a non-number (and thus treated as a non-day), but if one of the other columns cannot be parsed as an integer, the program will fail with a not very readable stack trace. (As it will fail when attempting to calculate the average temperature) You might want to add a check for this that raises a nicer exception.
• The pipeline on line 22 does not make the function more readable. Simply doing Enum.map(row, fn x -> ... end) is probably better.

So, those were my nitpickings ^^'. In my opinion, you’ve done great on this exercise.