Both genitive forms are possible, depending on the context. Sometimes, particularly if it's matter of possession, the genitive form of the possessor noun is dependent on whether it's a singular or plural entity:
(1) The winner’s medals were stolen.
(2) The winners’ medals were stolen.
In (1) and (2), the nouns "winner’s" and "winners" are functioning as determiners. In (1) the medals belonging to just one winner were stolen, and in (2) the medals belonging to more than one winner were stolen, and the genitive markings, respectively -'s and -', correctly reflect that.
Sometimes, it's not a matter of possession, but one where the noun in the genitive case is being used to modify another noun in which case we talk of its 'attributive' use as opposed to its use as a determiner. Consider these examples, the last one with "winner":
(3) They've just moved to an [old people's home].
(4) I've sent off for a [Sainsbury's catalogue].
(5) These very expensive [ladies' gloves]
(6) He had quite a collection of [winner's medals].
In (3) - (6), the genitive case has a different meaning to that in (1) and (2). In (3) it's a home lived in by old people; in (4) it's a catalogue produced by Sainsbury's; in (5) it's some gloves that are worn by ladies and in (6) it's a collection of medals that were awarded to a winner in some competitions. In each example, the underlined nouns have nothing to do with possession.
Attributive genitives are unusual in that they are a somewhat unproductive category. For example, while it is possible to have a summer's day and a winter's day, corresponding forms for the other seasons are quite marginal, for example these would be unacceptable for most speakers: a spring's day; an autumn's day. Similarly, we have a ship's doctor but not a school's doctor (instead we have a school doctor.)