Ok so this is what you can do:
In your EditorTemplates
folder create a template called DateTime.cshml
(the name will resolve automatically if you use it for dates, otherwise you have to specify it when using it).
Then in it:
@model System.DateTime
@Html.TextBox(
string.Empty,
Model.ToString("yyyy-MM-dd"),
new { @class="datepicker", @type = "date"})
Using the last parameter you can specify any html attribute (class, data, type etc.).
Then you use it like this:
@Html.EditorFor(x => x.ADate)
In case you chose to name your template with a different name you can specify it by invoking another overload:
@Html.EditorFor(x => x.ADate, "MyOtherAwesomeTemplate")