Mixed Seeds have been available in Stardew Valley from the very beginning. You can find Mixed Seeds by tilling special dirt and sand tiles with wiggling grass sprouts, or by chopping or harvesting weeds. If you plant them, Mixed Seeds will grow into a random low-cost plant type based on where you are and what season you're in.
The 1.6 update to Stardew Valley switches things up by creating a special new category of forage-exclusive seeds. Like Mixed Seeds, you can only find them through foraging, but unlike Mixed Seeds, you know exactly what crop you're getting. Plus, you can't buy them from any store. For the season of spring, the special forage crop is 
Carrots.
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Where to Find Carrot Seeds
The best way to find Carrot Seeds is to go looking for special sand and soil tiles with wiggling shoots. These tiles are much more likely to contain special items such as clay, Mixed Seeds, artifacts, and Carrot Seeds. Carrot Seeds can appear in any region of Stardew Valley itself, along with Calico Desert, but they won't appear on Ginger Island. Weeds are another source of Mixed Seeds, but they don't appear to drop Carrot Seeds.
The time of year is another important factor. You're much more likely to find Carrot Seeds near the end of winter and during the first two weeks of spring. If you look for Carrot Seeds during the end of spring, you'll find Summer Squash Seeds instead (as the name suggests, Summer Squash are the forage seeds for summer).
You can also get Carrot Seeds as a special reward. For instance, the first reward in Mayor Lewis' prize box is a set of 12 Carrot Seeds, which you're likely to get in the spring of year two (at least, if you keep winning the Egg Hunt). Carrot Seeds can also drop from crates and barrels in the Mines, at least during the appropriate times of year.
How to Grow Carrots
Carrots take three days to grow, which means they're ready to harvest three days after the day you plant them. Like other crops, you can shorten the harvest time by using Speed-Gro fertilizer or increase the crop quality with regular fertilizer. As a root crop, Carrots will leave the soil once you harvest them, so you'll need more Carrot Seeds to keep the crop going.
The base value of a Carrot is 35g, and you can get double that amount if you manage to grow an iridium-quality Carrot. Like other vegetables, you can pickle Carrots in a Preserves Jar to get an item worth 120g, or you can get Carrot Juice by putting it in a Keg. The base value for Carrot Juice is 78g. All of these values are identical to Parsnips, but (unlike Parsnips) you don't have to buy Carrot Seeds.
Stardew Valley
- Released
- February 26, 2016
