You're wrong about extension methods accessibility, but beyond that, you should write a class that provides the functionality you need.
public class Birthday
{
public DateTime MyBirthday { get; set; }
public Birthday(DateTime date)
{
this.MyBirthday = date;
}
public bool IsBirthday(DateTime date)
{
return (date.Day == MyBirthday.Day &&
date.Month == MyBirthday.Month);
}
public Weekday GetBirthdayWeekday()
{
return MyBirthday.DayOfWeek;
}
}