I have this problem as well. Unfortunately, while the alternatives described by Ethmoid are well laid out, the statement "there is nothing else you can do but…" implies that 1) this problem is a result of our use of "old" technology and that 2) it was unavoidable.
First of all, saying Snow Leopard is outdated is insufficient and irrelevant - many of us on the forum were all using it and willing to make sacrifices to do so - i.e., we could make choices to decline updates etc so we could still keep our software/devices/workflow compatible with Snow Leopard - if something requires iTunes 12.2 or OS X 10.11 we choose not to use it. Everyone's happy. The fact that it is "too old" just means "don't do the update".
Second, and more importantly, the manner by which the problem occurred resulted directly from Apple, not us, and I would like an explanation. We were invited to update iOS to 9.0.X. That there was no strong warning about needing a particular minimum version of iTunes is distinct from there being no warning that "the current version of iTunes you are using will render this Phone not useable on this computer". Every other software update I can think of I have ever done on any platform will have you update the prerequisites (i.e. iTunes 12.2/12.3) FIRST if they are required for the main update (i.e. iOS 9.0.X) to function. (And of course at this point we could have stopped, and still used our iPhone and computer happily.) In fact, allowing a device-software (iPhone) to update to a state in which it is no longer useable by the application-software (ITunes) that CONTROLS THE UPDATING would seem to disastrously fail basic, good programing or procedural practices. I was honestly highly surprised when I got that error message realizing that this is what just happened.
As mentioned in the first point, I and others make choices to maintain the computing environment that best suits us. In this case, the choice was taken away. In essence I feel like I've been tricked and/or that Apple did not sufficiently think through a very basic principle of not updating a device out of usability by the current system (without first requesting update of that system). Over the 22 years I've had Apple products, I never thought I'd question their software design capability or approach to customer, but this has done both, not to mention eliminating any reason for me to get an iPhone over another phone based on compatibility with my computer/files/etc.
Could someone please provide any insight of why the update was so (apparently) bizarrely and carelessly carried out in this manner (or if I missed the warnings?), and if it will be in the future, so we can make our choice on what computer/software to use in the future?
Thank you very much.