The property of being Landweber exact is independent of the orientation.  In terms of Landweber's criterion, this is generally phrased as saying that the element v<sub>n</sub> is invariant modulo the ideal (p,v<sub>1</sub>,...,v<sub>n-1</sub>), and so any change-of-orientation (which induces a strict isomorphism on the formal group law) does not change the property of v<sub>n</sub> being or not being a zero divisor after modding out the previous terms.

This follows from Lemma A2.2.6 in Ravenel's green book, which implies that any endomorphism of the formal group law over an F<sub>p</sub>-algebra R is of the form g(x<sup>p<sup>h</sup></sup>) for some h and some power series g.  In particular, the p-series [p]<sub>F</sub>(x) over R/(p,v<sub>1</sub>,...,v<sub>n-1</sub>) has this property, and so the leading coefficient v<sub>n</sub> is invariant under strict isomorphisms.