Today, the weather is crisp. I like this weather. It was a bit cold in the early morning when I left the house but I warmed up as I ran. I can run better in weather like this without quickly tiring (out).
We normally say "crisp". "Crispy" is a word we would use to describe a cold breakfast cereal. Nonetheless, "crispy" is not wrong.
If you avoid "get", your vocabulary will improve. It can almost always be replaced by a better verb. To discover what verb to use, look at your adjectives:
"I got warmer" can be replaced with "I warmed up".
"getting tired" can be replaced with "tiring out".
Instead of "it was a bit cold" (which is correct), you can say "it was a bit nippy".