Yes, you can use a 13" MacBook Pro for design—that is, depending on what type of design you are doing. Dreamweaver, InDesign, and Illustrator will all run just fine on one.
Photoshop will run well on a 13" MBP as well, though CS6 will run slower if you enable the "Use Graphics Processor" option in the preferences. Previous posts from others discussing the shortcomings of an integrated graphics processor are correct: The 13" MBP will pull from the RAM and use some of that memory as video memory. This method is slower than using a dedicated AMD or NVidia card. However, the Intel HD 4000 is a significant improvement over the previous Intel HD 3000.
After Effects will also run on a 13" MBP, but will not run exceedingly fast when rendering. The 13" MBP is only a dual-core i7, whereas the 15" offers quad-core. After Effects benefits from multiple cores. Additionally, After Effects really ought to have a dedicated video card for optimal performance. It will run on an Intel HD 3000 (I've tried it) but it's definitely faster on a "real" card.
I am not a fan of matte displays. While they are much less reflective, I personally prefer the more saturated colors of a glossy display. For print, the matte display is arguably better, as it can be better-calibrated to match printed output. However, I mostly do digital design work at this point and enjoy the look of a glossy display. I think the preference of a matte vs glossy display is a matter of preference more than one being "better" than the other. In my design classes of about 22 students, only one has a 15" MacBook Pro with the matte display option. The majority are running 15" MacBook Pros with the stock, glossy 1440 x 900 screen.
As for upgradeability, it is true that the 13" and 15" non-Retina MBPs are more upgradeable than the new Retina MacBook Pro (rMBP). Both machines will run 16 GB of RAM (Apple claims 8 but it's not true) and can hold a traditional hard 2.5" drive up to 1 TB in storage size. They both also work just fine with after market SSD drives, the largest I have ever tried being 512 GB from Crucial. If finances are a concern but you know you will upgrade components later, then a 13" or 15" non-retina might be the best for you.
If you choose to buy a 13" or 15" without a retina display, please be advised that while opening the case does not violate your warranty, the chassis are made of aluminum, including the screw holes used to hold the bottom plate on. I say this because if you are going to upgrade parts yourself, I HIGHLY recommend that you do it all at once and only take the panel off one time, put in your new components, then be done with it. It is unbelievably easy to strip those screw holes, and then you're hosed. Do not under any circumstances overtighten the screws. You will have to replace the entire topcase because of the Unibody design, and that is pricey. Opening the case is permitted under the warranty, but Apple will not replace it for free if you strip a hole.
The rMBP is very nice and has a higher contrast ratio than even the matte 15/17". The downside is that no Adobe apps are currently optimized for the retina screen, it's not upgradeable, and legacy ports are non-existent. Personally, I welcome the changes because it makes the machine much lighter and I do a lot of traveling. Some folks have commented that they need/want a DVD drive, ethernet, etc. That may be true and that's fine; each user has different needs. Me? I can't remember the last time I needed to burn a DVD. I buy Blu-Ray now, so even watching movies is a no-go for me on a Mac. I haven't been tetherd via ethernet since the early 2000s, and welcome the wireless-only approach from here on out. But that is just my experience. Again, it's really up to you and what you need.
Bottom line: the 13" MBP is a fine machine and will do you fine for design work in most cases. I would recommend a 15" or better, however, if you plan to keep it for the long run and will do a lot of video and/or After Effects work.