you don't need to open them to save them.
to make things as simple as possible
use my computer, explorer or open my documents and then my pictures
then in the file menu (top left)
file | new | folder
when the folder appears type in a name - USGrandkids (or whatever suits you)
LEAVE THIS WINDOW OPEN
then open your e-mail
right click the attachment | save target as
find the folder you made and OK
next time you'll already be in the right folder .... so just keep going 'till you have them all.
switch back to the folder you created .... from the top menu
View | thumbnails.
make certain you have all the pictures
(consider putting them on a CD or DVD as well
then you can deal with the mails ....
personally I'd then do as teram says and store the mails in a folder in your hotmail account (unless there are 1000000s of them)
that way if something happens you have a backup of the backup