All IP addresses (and, in fact, all multi-byte numbers used in the standard networking stack) sent on the wire are in "network order" which is big-endian.
How to represent four bytes of anything within a program depends on the programmer though they typically let the compiler decide which of course uses whatever the native hardware uses.
From Why is network-byte-order defined to be big-endian? ...
RFC1700 stated it must be so. (and defined network byte order as big-endian). It has now been superseded by RFC-3232, but this part remains the same.
The convention in the documentation of Internet Protocols is to
express numbers in decimal and to picture data in "big-endian" order
[COHEN]. That is, fields are described left to right, with the most
significant octet on the left and the least significant octet on the
right.
The reference they make is to
On Holy Wars and a Plea for Peace
Cohen, D.
Computer
The abstract can be found at IEN-137 or on this IEEE page.
Summary:
Which way is chosen does not make too much
difference. It is more important to agree upon an order than which
order is agreed upon.
It concludes that both big-endian and little-endian schemes could've been possible. There is no better/worse scheme, and either can be used in place of the other as long as it is consistent all across the system/protocol.
