Carry wire cutters, but only cut the wire if life is at stake, as others point out, the wire is there for a good reason and cutting it might result in prosecution or being shot at.

To cross without cutting the wire, a forked stick to lift the bottom strand and keep it lifted whilst you wriggle underneath can help.

Another possibility is to carry a couple a pieces of expanded foam pipe insulation, slip these over two strands of the wire and squeeze between, with little risk of snagging.
The insulation material is rather bulky to carry, but very lightweight.

In many cases the barbed wire fence needs to be crossed without undue delay.
If however delay is acceptable, then cross at the hottest time of day since the wire will have expanded and be slightly less tight.