A reader a few weeks ago asked me to do a post on Saudi women. I don't think this will be very good, considering that women in every country are so diverse... but I will give it a go.
The reader's main point was that a lot of Saudi women in foreign countries (on scholarship, etc) seem quite stand off-ish so it's hard to get to know them. I think that sort of perception is definitely a valid one but of course then we need to put ourselves in their shoes where they're living in a country that's very different to Saudi so we are coming at it with a different perspective than they are (social interactions, etc).
So... forgive me in advance but here is my best shot at giving a very limited insight. Saudi women can be extremely shy & quite up-front as well. Most that I know are also quite blunt & strong. Remember that this is what has been shown to me, I obviously have no idea what any woman anywhere is actually thinking. I would say it's probably a fair assumption as well to say that many Saudi women know how to be patient (sabr) and definitely know the virtues of being so. They can also be very kind and giving - e.g., between friends in my own country, a gift could be some flowers or a small piece of jewellery. From my own experiences, it's not uncommon to receive gifts like expensive jewellery, mobile phones, etc from good friends in Saudi. That's not to say that only rich people give those things because I only know lower to regular middle class people and they would save to purchase that for a friend. So there's definitely a big importance placed on friendship/gift giving.
The reader also wanted to know (I'm guessing) how to befriend them coming from the perspective of a foreigner marrying a Saudi. My answer to that is don't overanalyse it! Saudi women are people just like us - there may be cultural norms/expectations that we don't obviously know about or practice but chances are they are feeling the same way.
This is a poor excuse for a post but really I can sum it up by saying that Saudi women are women and you can't really present a post analysing a group of women, we all know what a huge post that would be (and that it'd probably be waaaay off the mark!) - so my point is that if you feel someone is stand off-ish, then break the ice a bit! It doesn't hurt to get out of your comfort zone, you can make some great friends for life out of it inshaAllah. Take the nationality out of the equation and you are answering your own question, really.