As you can see on Occurences Hörler in Switzerland Hörler is a typical Appenzell name - with families holding citizenship since before 1800 in catholic Appenzell as well as reformed Speicher and Teufen. That you have postcards from Teufen might be an indication your family came from there.My Great Grandmother was Anna Horler (the o has two dots). When they arrived here it was spelled Hurler. I have postcards from Teufen (Switzerland) from early 1900. Anna Horler's Father was Jake (Jacob) Horler & Anna was his wife. Can you direct me to a chat or where to send to request information.
Now, before I can give more detailed advice, it would be useful to know more about what you know already: when (at least guesstimated) was your ggrandmother born? When did the family emigrate? Anything else?
If they left after 1876, the civil registry office of Teufen will have them on their register (if they actually were citizens of Teufen) - so this would be the first place to ask. If they left well before 1876, it might be worth enquiring about what can be found in the Billeter collection: as this is a secondary source it has to be treated with some caution - but it is a very useful starting point for your own research; however, it usually stops around 1900 or even before.
Janice sucht nach Angaben zu den Vorfahren ihrer Urgrossmutter Anna Hörler, Tochter von Jakob Hörler und seiner Frau Anna. Janice hat um 1900 aus Teufen geschriebene Postkarten, was ein Hinweis darauf sein dürfte, dass die Familie von dort kam: Hörler sind seit vor 1800 Bürger von Teufen (siehe Vorkommen Hörler in der Schweiz).
Für weitere Hinweise müsste mehr darüber bekannt sein, was schon bekannt ist. Je nach Auswanderungsjahr könnte dann das Zivilstandsamt oder auch die Billeter-Sammlung die erste Station bei der Forschung sein.