Well dropdown list will be rendered in browser as html select and with the html select as far as I know you can not do what you ask for.
Instead, you can build your own control that has a readonly textbox and a listbox. You can limit the height of the control by setting the height property of the listbox.
OR you can use ListBox control and set the height of it to show 10 items.
OR you can also use AJAX AutoCompleteExtender
**Maybe you can try to do pagination on the data source for the drop down list using PagedDataSource and set the PageSize to 10.(Not sure about this one)
Also,
<asp:DropDownList ID="DropDownList1" onmouseover="this.size=10;" onmouseout="this.size=1;" runat="server">
</asp:DropDownList>
can help you a bit but may not cover it all.
I hope these are helpful.
Good luck,
OI