Never attempt to parse the output of ls for anything other than display purposes --- it is a bad idea.
Though it uses find and xargs instead of sed, maybe something like this would work. Note that it is untested.
jan01="$(date -d '20100101 00:00' +%s)"
feb01="$(date -d '20100201 00:00' +%s)"
today="$(date -d '23:59:59' +%s)"
daysecs="$((24*60*60))" # 86400
dayssincefeb01="$(((today - feb01) / daysecs ))"
dayssincejan01="$(((today - jan01 + 1) / daysecs ))"
find /path -type d -mtime +"$dayssincefeb01" -mtime -"$dayssincejan01" \
-print0 | xargs -0 rm -r
The find command at the end finds directories that are older than 01 Feb 2010 but younger than 01 Jan 2010 and pipes them safely to xargs using the '\0' null character.