Is opening/closing cards really going to have a negative effect on my getting a mortgage? The broker said our credit rating is so good, all we have to do is find a house. I pay my balance in full every month.
In my opinion, this isn't about whether it WILL, it's about whether it COULD (and if it does impact your rate, that will be VERY VERY expensive). It's kind of like having an inexperienced pilot land a 747... There's no guarantee anything goes wrong, but if it does, it's very likely to be fatal. So even if you believe it's a "low to medium" likelihood, it's a "very high" impact...
Thus: Don't change anything - open OR close. Both can impact your credit. If it's good now, don't mess with it.
You credit is based on a few things: utilization (how much of your credit you use), average age of account, payment history, number of hard pulls.
Opening is especially problematic, as not only does it create a new "hard pull", it could give a big spike downward in average age of account, especially if you only have a few cards.
Mine plunged about 60 points over the first 4 months when I started playing the points game. 15 months later it has basically fully recovered (though I haven't opened a new card in ~6 mo). My utilization is MUCH lower, my average age of account is maybe 1/3 of what it used to be but is still tolerable given the other metrics. Hard pulls are bad for the first few months, then they are present on the account for like 2 years, but their impact degrades fairly quickly.