What are some good ways to lightly reference crop growth patterns/farming seasons?

Knowing just crops in particular and the climate your story takes place in would be quite helpful.

Here's a general guideline for some of the more common ones.

Alfalfa (and most other hay crops) can be planted basically anytime although the most common times are early to mid-spring and sometimes mid-summer and is harvested a few times during the summer. This is highly variable by climate and latitude.  longer summers = more cuttings are taken.  Anywhere from one harvest halfway into Canada to 8 or 9 in the deep south.  Most of the main alfalfa growing areas it's 3-5 cuttings, spaced a little over a month apart.

Corn is planted later in the spring once the soil's warm and harvested mid to late fall.

Soybeans are planted and harvested shortly before corn.

Oats are planted early spring, and harvested late summer or early fall.

Winter wheat and rye are planted early to mid fall and harvested mid summer.  In colder climates they need to grow spring wheat (ND, MT, prairie provinces, etc) with a growing cycle similar to oats I believe.

Remember this is just very basic, but should be enough to just touch on for your story.