If I designate an item before Shabbos for an acceptable purpose, it can become not muktza for me. Can another person, whom I did not have in mind when I made my initial declaration then use that item?
My specific case is that snow fell on Friday and I designated that I would be using the fallen snow to make snow cones (snow+grape soda!) on Saturday. No additional snow fell between designation and consumption. Some were hesitant to try one due to muktza concerns.
I will try to answer without getting into the specifics of snow, as that was only an example for a general question
It would seem that designation of an item before Shabbos (if done according to the stipulations in the Shulchan Aruch) means that it is allowed for everyone to use.
See Orchos Shabbos (3:19:127) who rules that even though medication that is not regularly used is muktza, if a person in the household was sick before shabbos and he needs this medication, then the medication is not muktza anymore for everyone, as the Hachana- preparation before Shabbos made it not muktza.
In the footnote the Orchos Shabbos cites the Shulchan Aruch in 318:2 who allows a healthy person to eat meat of an animal slaughtered on Shabbos for a sick person who needed such meat, regardless of if the person was sick prior to Shabbos already. (My addition- see Mishna Berura there (318:8)
שחלה היום - ולא אמרינן דהבהמה היא מוקצה מחמת איסור דאיתקצאי בבה"ש מחמת איסור שחיטה שבאותו פעם לא היה חולה עדיין שיהיה דעתו עליה לשחטה דהא אנן קיי"ל כר' שמעון דלית לו מוקצה אלא היכי דדחיה בידים כגון נר שהדליקו עליו באותו שבת דדחיה בידים שלא להשתמש בו באותה שבת כיון שהדליק בו אבל גבי בהמה לא דחיה בידים ועיין עוד בב"י
meaning, that the reason it is allowed to be eaten by the healthy person even if the other person became sick on Shabbat is because we rule like Rabbi Shimon and the animal was never "really" muktza. Based on that Mishna Berura, if the item is "really" muktza, then it would still not be muktza, given that the person was sick before Shabbos. And as stated in the Shulchan Aruch even the healthy person is allowed to eat the meat.
Additionally, the Mishna Berura 38:91 can also be a source for such a Heter
(צא) או בבקעת וכו' - וה"ה אם רוצה לסמוך בקורה את הדלת צריכה יחוד כמו בבקעת ואז איכא תורת כלי עליה [אחרונים]
The context of this Mishna Berura is the Shulchan Aruch who discusses how one can prepare a muktza item to be not muktza for Shabbat. The Mishna Berura writes that once it is prepared correctly it איכא תורת כלי עליה loosely translated, the item has the status of a vessel. Once an item is a vessel, it loses the status of muktza for everyone, as it wouldn't be any different to any other permitted vessel (for example, a cup).
