As far as I’m aware there is no evidence to space out vaccines, either in horses or humans. There also is a downside–splitting up vaccinations increases the chances that the second set of vaccines is going to be missed or not done in a timely fashion. In my part of the world, I’ve never heard of reputable farms splitting up vaccines and horses worth 6 figures are routinely given all of their spring vaccines at once.
I would not use a vet that recommended splitting up vaccines, because I would be concerned that they either 1) were not knowledgeable or 2) were knowledgeable but unethically recommending something unnecessary to either charge more $$ or to curry favor with anti-vax nut job clientele. That’s fine with me if a vet wants to cater to anti-vaxx clientele as a customer service issue (and realistically many vets probably do have to deal with this), but that’s not a good fit for me as I prefer to follow evidence based practices.
The only exception to this rule would be the intranasal strangles vaccine, which you would not want any residue from that to contaminate any intramuscular injection sites and you would want to follow your vet’s advice as to what precautions should be taken.
When in doubt, you can always refer to the AAEP website which has a very informative section on vaccination.