SQL Server date format not working for stored procedure

I have a stored procedure that updates a row in a table. I'm using C# to pass all the parameters into the stored procedure like this:

public int editFestival(String festId, String festNaam, String festLocatie, String festDatum,
                        String festDuur, String festEindDatum, String festUrl)
{
sqlConnection = new SqlConnection(ConfigurationManager.ConnectionStrings["project"].ConnectionString);
sqlCommand = new SqlCommand("EditFestival", sqlConnection);
sqlCommand.CommandType = CommandType.StoredProcedure;

sqlCommand.Parameters.Add(new SqlParameter("@festId", Convert.ToInt32(festId)));
sqlCommand.Parameters.Add(new SqlParameter("@festNaam", festNaam));
sqlCommand.Parameters.Add(new SqlParameter("@festLocatie", festLocatie));
sqlCommand.Parameters.Add(new SqlParameter("@festDatum", Convert.ToDateTime(festDatum)));
                                 //Also tried ->       , SqlDbType.date)).Value = festDatum
sqlCommand.Parameters.Add(new SqlParameter("@festDuur", Convert.ToInt32(festDuur)));
sqlCommand.Parameters.Add(new SqlParameter("@festEindDatum", Convert.ToDateTime(festEindDatum)));
sqlCommand.Parameters.Add(new SqlParameter("@festUrl", festUrl));

sqlConnection.Open();
sqlTransaction = sqlConnection.BeginTransaction();
sqlCommand.Transaction = sqlTransaction;
rows = sqlCommand.ExecuteNonQuery();
sqlTransaction.Commit();
return rows;
}

Although the String festDatum (which means festDate in english) is in a correct format (yyyy-MM-dd) it's not accepted by the stored procedure.

When I execute the stored procedure with my own given variables, this is what it generates:

USE [groep2_festivals]
GO

DECLARE @return_value int

EXEC    @return_value = [dbo].[EditFestival]
        @festId = 1,
        @festNaam = N'Rock Werchter',
        @festLocatie = N'Werchter - Belge',
        @festDatum = 2013-07-01, --This is where it says that there's a syntax error near '-'
        @festDuur = 4,
        @festEindDatum = 2013-07-04,
        @festUrl = N'www.rockwerchter.be'

SELECT  'Return Value' = @return_value

GO

When I manually surround both dates with single quotes it works fine. What am I doing wrong? Or would it be as simple as surrounding the parameter inside the update statement with single quotes?

EDIT: This is the original stored procedure (should have posted this earlier)

USE [groep2_festivals]
GO
/****** Object: StoredProcedure [dbo].[EditFestival] Script Date: 10/05/2013 12:44:49 ******/
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
-- =============================================
-- Author: Robbie Vercammen
-- Create date: 10/05/2013
-- Description: Veranderd de gegevens van een bepaald festival
-- =============================================

CREATE PROCEDURE [dbo].[EditFestival]
    (
    @festId int,
    @festNaam nvarchar(255),
    @festLocatie nvarchar(255),
    @festDatum date,
    @festDuur int,
    @festEindDatum date,
    @festUrl nvarchar(255)
    )
AS
BEGIN
SET NOCOUNT ON;
UPDATE festivals
SET fest_naam = @festNaam, fest_locatie = @festLocatie, fest_datum = @festDatum,
    fest_duur = @festDuur, fest_einddatum = @festEindDatum, fest_url = @festUrl
WHERE fest_id = @festid
END

EDIT: What I'm trying I execute the stored procedure from within management studio

The generated code is already posted above ;) When executing that it just says

Msg 102, Level 15, State 1, Line 8
Incorrect syntax near '-'.