It depends on a few things. Different bulbs/plants have different zone hardiness ranges. Many fall bulbs will be fine, but check the zone rating for the type you are wanting to plant. When grown above ground in a pot, the bulb's hardiness zone rating needs to be about one zone colder than the zone you're in. Since the weather patterns have shifted in this part of the country, you are likely at least one zone hotter than the official map shows. These two considerations may cancel each other out.

Well draining soil is important. Be sure to use a well draining potting mix in your container. A normal good potting soil mix should be OK for this.

The size and type of container can make a difference. Larger containers will experience less temperature change (which is desirable). Clay containers will be a little better than plastic because the clay can hold a little heat.

Finally, the location can make a difference. The amount of sunlight, the timing of sunlight (morning, afternoon, or all day), and microclimates can all play some part in this.

Another problem can arise because of clay splitting during freeze/thaw cycles.

I plant bulbs in containers every winter. I also have lots of clay pots that stay out during the winter. But I plant most of my bulbs in plastic, and I am not surprised when I lose a couple of the clay pots over the winter.

High quality terra cotta (thick walls, high fired, well made) will be less likely to split than the cheap stuff -- but you'll always be at risk with clay, because of the nature of the material. Water molecules get into the pores of the clay, then expand when they freeze -- leading to cracking and splitting. Them's the breaks!

Many large clay pots are double-fired and guaranteed not to crack from freezing. If they are double-fired, they shouldn't crack.

Thanks to all of you for your responses. I'll let ya know how it goes.

I've got a lot of pots with bulbs in them. A tulip/daffodil already has the little flower inside of it when you get it. It's hard not to have them bloom the first year, no matter what you do, unless they're dug up by thieving, pillaging squirrels who will sit and eat them while looking at you!
I haven't had a problem with large, heavy clay pots cracking. By large, I mean 12 inches or more in diameter. I usually get the "azalea" pots which are wider than they are tall. I've got some I've had outside year round for 4 years without any problems. They work great for bulbs as well as violas and Impatiens.
Spring bulbs need a certain amount of freezing and cold to be triggered to bloom. They're very hardy and can stay out in the coldest weather.

One of my favorite clay pots cracked last winter, alas. About 2 1/2 feet tall, about 18" diameter. Cracked in two big pieces. Sigh.

You are at less risk with high quality pots. But few of the pots people buy -- especially at the big box stores -- are high quality. Good terra cotta can be VERY expensive, unfortunately!

Geez ya'll where is the WS advice?

Vol Law, try Winter Sowing. It's easy; you just make an individual mini greenhouse. Most all of us Winter Sow in some form or fashion and there is even a WS Forum on GW to help as well.

I'm already saving my Gatorade jugs!

Well, ya see, she was asking about BULBS -- not seeds...... ;-)

Can you not WS with bulbs?

Well, you don't really need to "WS". Ya just stick the things in the ground, and the bulbs take care of the rest. ;-)