Q. Are nuts prohibited on Rosh Hashana only, or on all the Ten Days of Teshuva?

A. There are different minhogim mentioned by Poskim regarding the time one keeps this tradition.
From Remoh’s (O.H. 583: 2) citation of the minhag, it would seem that it applies only to Rosh Hashono. However, Nitei Gavriel (Rosh Hashana 6: 8, quoting Beis Hayotzer and others) mentions that some observe it during the whole month of Elul until Hoshano Rabbo. Others maintain only from the beginning of selichos (Ktzei Hamateh and others). Chassam Soffer would restrict the minhag only to Rosh Hashono itself, while his Rebbe, Horav Nosson Adler zt’l only until the second day at chatzos. (Piskei Teshuvos 583: 7). See next question in regards to the reasons of this tradition.
Horav Shlomo Miller’s Shlit’a opinion is that one should maintain his family’s and community traditions.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a