I think the number of items is not the crucial parameter. First, you should decide whether the filter is appropriate to the interaction.
The decision could be based oh two important parameters, which are User and Data related. This two dimentions are presented on the picture:
User-related
Filter is the mean to make selection faster. Users, which are competent in subject field, know what to search and filter allows to perform selection task in a faster way. Non-competent user doesn't know what to search and his interaction looks like exploring and then selecting.
Data-related
Second dimension is the nature of data. If the data if highly structured, user could perform selection task in a fast way, even without any support. Under structure I mean ordering, sorting, or some other organization of the data. This organization helps to navigate and select required item.
Non-structured data requires support to make selection task faster, and filter could be such supporting tool.
Examples
Competent user, Structured data (visual support by country's flag and language) – no filter.
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Competent user, Structured data (natural ordering) – no filter.
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Competent user, Weak-structured data (different type of data: city, district, region) – filter needed.
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Non-competent user (in exact category naming), Less-structured data (alphabetical ordering adds value) – no filter.
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Too many items – do not use dropdown!
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