find already has this functionality:
find . -newermt "2013-01-01 00:00:00" ! -newermt "2013-01-02 00:00:00"
From the manpage:
Compares the timestamp of the current file with reference. The
reference argument is normally the name of a file (and one of
its timestamps is used for the comparison) but it may also be a
string describing an absolute time. X and Y are placeholders
for other letters, and these letters select which time belonging
to how reference is used for the comparison.
a The access time of the file reference
B The birth time of the file reference
c The inode status change time of reference
m The modification time of the file reference
t reference is interpreted directly as a time
Some combinations are invalid; for example, it is invalid for X
to be t. Some combinations are not implemented on all systems;
for example B is not supported on all systems. If an invalid or
unsupported combination of XY is specified, a fatal error
results. Time specifications are interpreted as for the argu‐
ment to the -d option of GNU date. If you try to use the birth
time of a reference file, and the birth time cannot be deter‐
mined, a fatal error message results. If you specify a test
which refers to the birth time of files being examined, this
test will fail for any files where the birth time is unknown.