Oh, I forgot to mention in my previous post - if you want to avoid spiders, definitely do not go in and watch "It's Tough to Be a Bug" in California Adventure!! That is not a show for you.
I am trying to think about any spiders that might be in Haunted Mansion Holiday. The thing with HMH is that it is is much brighter and more colorful than the regular Haunted Mansion. It's got a crazy mixture of Halloween and Christmas decorations. It's a really thorough overlay - the whole ride is basically transformed from beginning to end, outside to inside. The 'creepy' factor is not as big as it is in the regular version of Haunted Mansion, so I don't think spiders are very obvious if they are there. I don't think I noticed any.
There is a big 'web' on the outside of the Haunted Mansion Holiday ride, but I don't think it has a spider in it. I'm trying to remember.