We have a jar of Hannah's Red Hot Pickled Sausages that we just opened last night. I couldn't find any "Refrigerate After Opening" indication anywhere on the jar, so we left them out overnight. I'm still uneasy about it, but the only way to ask Hannah's is to have a facebook account. I don't have one since I don't use facebook (yes, only person on the planet), so I was hoping you may know for sure.
I'm unfamiliar with Hannah's, but if they are pickled with vinegar you might be okay so long as you consume them within a few days. If it were dilly beans or gherkins I'd say you're probably fine (depending on the amount of vinegar) - but meat is a different matter.
Do they look anything like this (or have similar ingredients)?