The usual dropdownlist has no support for a horizontal scrollbar.
Have a look at these links discussing the same:
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Link 2[
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Link 3[
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Alternatives like putting it in a Div would be suggested in general, but that would not look clean and would not suffice your situation.
Only alternative, I can think of is to make a custom control of yourself where you take a textbox and div collectively to have a dropdown look and feel that can have customized size and scrolls.
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