Mice, a rottweiler, an arachnid and a few other assorted critters make sturdy reappearances in five board book versions of picture books. In Ellen Stoll Walsh's Mouse Paint, ``three white mice on a white piece of paper"" enjoy a colorful romp, while in Walsh's Mouse Count a similar gaggle narrowly escapes being served for dinner (Harcourt/Red Wagon, $6 each, 28p, ages 1-3 ISBN 0-15-200265-0; -200266-9 Sept.). Yet another mouse searches the animal kingdom for companionship--and finds an unexpected respondent--in Eric Carle's Do You Want to Be My Friend? (HarperFestival, $6.95, 32p, ages 2-6, ISBN 0-694-00709-9 Sept.). The rewards of industriousness are celebrated in a second Carle title, The Very Busy Spider; its embossed web brings a tactile dimension to his familiar collage artwork (Philomel, $9.95, 26p, ages 2-up ISBN 0-399-22919-1 Aug.). Finally, the canine in question is Alexandra Day's beloved Carl, who takes charge of a crew of toddlers in Carl Goes to Day Care (Farrar, Straus & Giroux, $5.95, ages 1-3 ISBN 0-374-31145-5 Sept.).