Growing in pots means plants are at more risk if temperatures fall below freezing day and night for a week - there's a risk the potting medium will freeze, killing the plants within. Although you speak of 'frost' in winter, having checked the average temperatures in your region, it doesn't look as if the temperatures often go down below zero degrees centigrade.
Most of the mediterranean type herbs, such as oregano, thyme, basil and sage will be fine, but you will need to water frequently in summer, or any time when the weather is sunny and hot. In the ground, many herbs grow well in dry regions, but in pots, its a different matter, so watering twice a day may be necessary to keep them alive. You need also to take account of the growth habit of each herb; Rosemary, for instance, should be fine, but will need a pot to itself because it becomes a pretty large, woody shrub, whereas Oregano does better in wider, more shallow pots because of its low growth habit and widespreading nature. Sage also spreads out, but does tend to develop a woody base over time. Thyme comes in different varieties, some of which behave like ground cover, others forming a small bush above ground. Laurus nobilis (Bay) will be fine, but it becomes a tree, particularly in warmer climates.
Many plants classed as herbs are not intended for culinary use, but have been and are used for medicinal (herbal) or purely decorative purposes, such as Tanacetum and Lavender (although Lavender flowers are edible). Lavender should be fine with your climate.
Potting compost in the pots should be free draining, and the containers you choose should have drainage holes in the bottom. With regard to other herbs, its probably easiest if you ask about specific ones if you want to grow them - there are hundreds of plants classed as herbs, so I've just chosen a few which are commonly used in cooking and which will do well in those conditions.