您可以根据Month和Year提供要过滤的查询。

var monthlyCount = (from car in context.CarInformation
    where car.CurrentSituation== "Finish" 
        && car.InvoiceDate.Month == DateTime.Now.Month
        && car.InvoiceDate.Year == DateTime.Now.Year 
    select car)
    .Count();

label1.Text = Convert.ToString(monthlyCount);

请注意，如果没有materialize (immediate execution) the query，则不会执行当前的LINQ查询。
注意，COUNT查询可以用Count<TSource>(IEnumerable<TSource>, Func<TSource,Boolean>)的方法语法编写：

var monthlyCount = context.CarInformation
    .Count(car => car.CurrentSituation== "Finish" 
        && car.InvoiceDate.Month == DateTime.Now.Month
        && car.InvoiceDate.Year == DateTime.Now.Year);

正如@Svyatoslav Danyliv所建议的，要通过提供日期范围过滤器来利用索引用法，应该是：

DateTime now = DateTime.Now;
DateTime startDate = new DateTime(now.Year, now.Month, 1);
DateTime endDate = startDate.AddMonth(1);

var monthlyCount = (from car in context.CarInformation
    where car.CurrentSituation== "Finish" 
        && car.InvoiceDate >= startDate
        && car.InvoiceDate < endDate 
    select car)
    .Count();