Tazetta species originated around the Mediterranean basin, and thus their progeny prefer weather and soil conditions similar to the ancestral homeland. As much of the Mediterranean region is karst, or limestone, topography, most tazettas prefer a more alkaline soil. In general, the happy pH range for the fall and winter bloomers seems to be 7.8 to 8.0; the late winter bloomers seem to prefer a pH range of 7.4 to 7.6. Paperwhites, however, are more of a generalist type group and will grow well in a closer to neutral if not slightly acidic soil, but always love a good shot of wood ash as fertilizer.
Tazettas are somewhat cold hardy, down to 24* F without floret damage (if not prolonged and if no frost/ice). Watering repeatedly two to three days in advance of a hard cold snap will ensure the plants have as much water as possible in their leaves and stems. This turgor pressure will help to keep stems from bending. If they do bend, you can use a shish kabob skewer as a stake and tie up the stem to ensure sap flows to the florets (it works!).
However, frost is a different issue. The foliage will need protection from frost, as the small damaged spots become susceptible to fungal attack in very damp climates . Though easily treated by fungicide spray, it is easier to protect the foliage with frost cloth. Planting tazettas in a location on the south side of a tree canopy, which breaks up the settling of frost, can work well.
Ice and snow, and prolonged periods well below freezing, are altogether a different story. Florets encased in frost can rebound, and even in snow if it's only for a morning. Multiple days below freezing, with or without ice/snow, will toast the flowers and stems for the season. If it's really bad, you'll lose the foliage too. But, if a bulb hasn't yet sent up stems, you might get a late season bloom.
Tazettas, little oddballs of nature that they are, keep growing their foliage for most of the season. In the coastal south, that means six months or longer. This annoying habit allows the bulb to offset a hard freeze in the long term - it may lose its bloom but the new foliage ensures the bulb rebounds for the next season. In Atlanta, the paperwhite 'Miss Linda' froze completely to the ground in more than one season (temperatures at 8*-10*F), to later rebound and have a good bloom the following season. However, multiple hard freezes in a single season will substantially sap the bulb. If your climate has multiple hard freezes (below 21*) in a season, consider growing in large containers that you can move indoors as needs be.
Tazettas are heavy feeders, and need to be nourished accordingly. They are much happier in very well draining soil, to offset summer rot. Summer irrigation systems are a definite no-no. They are quite happy being overplanted with drought-tolerant summer annuals (which don't need much watering) that can be removed when the foliate starts getting of size. Fall ferilizing with 5-10-15 or 5-15-25 is a good idea. If commercial fertilizers are not your thing, a good 1/4 inch of wood ash is always appreciated. Tazettas grow like irises - their roots go out, not down. So spread your fertilizer out around the bulb for six inches or so.
Tazettas can be recalcitrant in storage as well. One variety stays as green as long as absolutely possible; one summer, bubs maintained green growth for a month after being "dried" for storage. Many varieties will sprout foliage at the first opportunity - like getting stored in the air conditioned house for a month before shipping, after spending a couple of months in the garage at 90*F. Others will sprout in hot storage if there's a prolonged rain event with high humidity. Thus, while temperatures in the 40*s will keep them rather dormant, dipping into the 60*s to low 70*s starts to feel like prime growing weather is around the corner and they'll break dormancy (along with really high humidity). So, if you are trying to maintain hard summer dormancy, keep the bulbs as hot, and dry (use a fan too!) as you can without direct sunlight.