choux pastry (puff pastry) is different from traditional pastry;
It has to be mixed a special way, but gets piped out then baked. It would be the most amenable to unsaturated veggie oils.
Most other pastry has to be rolled out and folded repeatedly. This makes things like danish pastry, baklava pastry, and pals.
There's also piecrust dough, which is a kind of pastry. This can easily be made with chilled veggie oil but the end product is inferior to those made with lard, tallow, or crisco shortening.
Then there is stuff like tortes and quiche-- Those are made from shortbread pastry dough.
The one thing they all have in common though is oil or fat of some kind. Again, it is NOT optional.

The oil is necessary for it to be pastry, and not hard tack.
http://en.wikipedia.org/wiki/PastryNote the chemistry section; Hard, stiff oils work better than liquid ones. (This is why freezing the oil to make it "goopy" can alleviate this, and produce a superior pastry with normally liquid oil, but again, requires one to work quickly.) This is one of the reasons why hydrogenated oils (Transfat and pals) are routinely used in making snack cakes and other processed food items; it's cheap, it's effective, and it wont anger vegans. (just health nuts and the american heart association.) The hydrogenation process turns runny vegetable oils into stiff, hard oils (that you cant digest, and which will clog up your arteries.)
There are some natural vegetable oils that would be suitable for making pastry without having to be chilled/frozen, but they often have strong flavors of their own:
Cacao butter,
coconut oil,
palm kernel oil, and pals. They are also, ALL OF THEM, very bad for you since they are loaded with saturated fat (which is also why they are thick and heavy/creamy lipids.)
Palm kernel oil is the cheapest of the three, and has the least offensive flavor. Cacao butter could be useful for some specialty pastries however, where the flavor of the oil would be of beneficial character (say, in pie crust for a chocolate creme pie); but would not be advisable for general pastry use. Similar with coconut oil.
*loves cooking. always has. Deserts especially.
Chilling the dough has more to do with supressing/retarding gluten strand formation (when used with runnier lipids) than it does with improving the working qualities of the lipid. Freezing the oil in the freezer will turn it into a "snot like" consistency, which can be used in conjunction with chilled flour and icewater/chilled milk to make a decent pastry; better than simply chilled dough alone can produce.