Do dried poblano/ancho chili have an expiration date?

Dried hot peppers lose flavor and heat over time. At ten years old, your poblano peppers are probably fairly bland. Smell them. If they don't smell bad, taste them. (Taste them cautiously; they may still have some heat.)

If they are completely tasteless, then there's really no point in using them. The wouldn't be harmful, they just won't add anything to your dish.

Worst case scenario, they have picked up some bad flavors from their time in storage. They may bring dusty or musty flavors to your dish. Or they may just taste like a generic mixture of all the things you have in your cupboard. If this is the case, throw them out.

Best case scenario, they still have some good taste, and possibly some spiciness. If this is the case, go ahead and use them. Use more than you normally would; use your judgement to estimate how much more than normal. If you also want the spiciness that your dried peppers are lacking, supplement with some hot pepper flakes or cayenne powder.

When you run out and buy more dried peppers, remember that the new ones will be much spicier. Use the new ones very carefully until you get used to using them, or you will over-spice your dish.