try:
=SUMPRODUCT((A1:A100>DATE(2000,12,31))*(A1:A100<DATE(2001,2,1)))
so if col A contains:
4/14/1999
4/13/2000
1/21/2002
2/13/1999
1/15/2002
4/18/2002
4/13/2000
2/18/1999
3/6/2002
2/3/2002
4/9/2001
2/23/2000
4/5/2002
1/29/2002
1/16/1999
4/12/2002
1/27/2001
2/5/1999
1/27/2000
1/6/2002
2/2/2001
3/23/1999
1/25/2002
2/7/2001
2/13/2001
1/12/2000
1/28/2001
1/2/1999
1/7/2002
1/13/1999
3/17/2001
2/23/2002
1/5/2002
3/13/2001
1/23/2000
3/9/2001
1/22/2001
2/22/1999
3/25/2002
1/18/2001
the formula returns 4