How to Convince IT to Let me Use MacBook at Work
They likely have little to no control over the designer's Macs, not because it isn't available but because they aren't knowledgable and don't need to worry about it for only a couple of people who require Macs out of necessity. This presents the concern for them that they wouldn't be able to properly manage and/or assist you. Whether or not the OS is more secure is irrelevant to them, they are already tasked with securing the Win 7 environment so the Mac would only present (potentially) more work for them as they would need to add management options for it or deal with it on a per help ticket basis.

Your best bet?

Get a couple of higher up executives/directors to ask for Macs as well. A higher percentage of people, especially when it includes those with influence, asking for Macs is much more likely to open the door than just one or two people.

My organization (roughly 500~ people, now about 200~ Macs) had this same situation, and what I just described is exactly what opened the door (which opened a flood of requests) for Macs.  Initially only the creative departments (working with video, publication, graphic design) had Macs, maybe 10-15 in the organization which used to be quite a bit larger.  4-5 years ago several of the directors and executives enjoyed the experience they had with their iPhones &amp; iPads so much that they started to push for Macs as their work computers.  Not long after MacBooks, MacBook Pros and iMacs were added as options for people to order when they were hired or due for a computer replacement.  Jump to now and Macs make up 35-40% of the organization.

The flip side, reason I have a job, IT was met with a new technology that they didn't know how to handle.  Macs were hogging bandwidth with software update downloads, Active Directory integration only allowed for some management, new Macs required a lot of effort to configure for use, no one was experienced enough to troubleshoot them properly, etc.  This made it a necessity to hire a Mac admin, which led them to me.  From what I understand desktop support has been much less stressed since I joined, which I can believe from the work I've had to do to "tame" the Macs.

Maybe not the answer you're looking for but I know of several other businesses that have had Macs approved in similar ways.  Hopefully the contrast of what it likely means for your IT team will help as well.