This is the 90th most frequent Japanese word.
まし
"まし" means "better," "preferable," or "less bad" in a relative sense.
Here, "まし" is used to suggest that taking action, even in an unfavorable situation, is better than taking no action at all.
そんな悪い状況で何もするよりは試みる方がましだろう。
In such a bad situation, trying is probably better than doing nothing.
Here, "まし" is used to indicate that the old car, while not perfect or ideal, is a preferable choice when compared to having nothing.
この古い車でもないよりましです。
This old car is still better than nothing.
In this context, "まし" expresses that rainy days, while not ideal, are the more favorable option compared to snowy days.