You should allow yourself to grieve and really allow that process to happen and not suppress it. Feel all those emotions and handle his things because they are imprinted in your heart and mind and he'll always be a part of you. That said, to balance with a positive, start looking - just to see what's available that would appeal to you. Therein lies the anticipation and a bit of
'moving forward'. Be sure to assess your personal taste in each horse and if it would be suitable for you at this time and fulfill your purpose and fit in at your barn. Yes, do take your time as far as not getting in a hurry and feeling compelled to find one within a time frame. Sometimes the looking provides a good distraction and you are moving forward by doing so. Just don't allow anyone to push you or take over your search and pick a horse for you. Alot of the joy and distraction is the process and the details. When you find the
right one, you'll know. My condolences -- losing an old one is so hard as is losing any age. Best of luck!
I don't think there's a right or wrong answer about how long to wait to get another horse for yourself. People deal with grief in different ways and at different paces.
Personally, it takes me a very long time to work through grief. While I've never lost a horse (I've only had my first horse about a year) I lost the dog-of-my-life to cancer in October of 2011 and it's only been in about the last two or three months that I can so much as look at dog-related stuff without bursting into hysterical tears, or think about buying another dog without feeling like it's a betrayal.
I think others' ideas on companion animals are good. And I think your heart will tell you when it is time to look for a new bond with a new horse for yourself.
I just wanted to thank everyone for their replies. I have taken all of this to heart. Luckily, my life schedule allowed me to be a zombie, not function normally and grieve at the time. My gelding has taken this way better than I expected. He is lonely and more affectionate than normal, but not obviously stressed. So I'm taking my time and trying to find the right horse. I may have missed out on some nice horses because I wasn't ready to actually go look at horse before now. It still hurts, I still miss her, but I am starting to move on.