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Beets in Arizona
If your beets were soft when you harvested them, you may have waited too long: Large beets (over 3 inches in diameter) can get soft, fibrous, or tough. Smaller beets (about 1 to 2 inches) are more flavorful and have a better texture. Medium beets (2 to 3 inches) are good for some purposes as well. For high-elevation gardens of Arizona (above 6000 feet), you can plant beets around mid-May through mid-June. Looks like your first expected frost date in autumn is about mid-September, and last expected is mid June. I believe the White Mountains are in USDA Hardiness Zone 6, which is not warm enough to have a winter crop. In certain lower elevations of Arizona (Zones 9 and above), one might be able to do so, however. Beets like it cool (60s F ideal for growing), and can withstand some frost, but they do not like a severe freeze.