Panoramic views from the top of Mt Mostiin Tsagaan (above), in the north of Ovorkhangai province, include the Mongol Els (sand dunes) winding like a yellow snake through the foothills. This region is renowned for steppe eagles and Graham spotted five while his horses grazed (above right) on a crisp autumn evening. Arkhangai province is famous for lush forests (left) that provide good fodder for hungry horses. The region also provides navigational hurdles and Graham was temporarily lost several times.

As I headed south on the second leg of my journey, the lush forests of the Bulgan province gave way to open, rolling steppe and as we entered Arkhangai province, pine trees clustered on the hillsides. An increasing number of small lakes began to appear and Samson and Goliath loved standing belly-deep in the cold water at every opportunity. But the need to get closer to the safety and warmth of Ulaanbaatar grew stronger as mornings became cool and crisp, and I resolved to travel faster. I felt in control now, able to pace the horses so they wouldn't tire too quickly.

On the first day of autumn an unexpected scattering of snow made me realise that sub-zero temperatures would soon be here to stay. I'd developed a pattern of travelling around 30 km each day, accepting the hospitality of local herders as well as camping out on hillsides to give the horses a good feed.

I was heading for Tsetserleg, the capital of Arkhangai province, and followed a marked road as I wound through increasingly hilly country. The sight of a mounted westerner was usually too good an opportunity for the locals to miss and I was often invited to tea or to stay the night and tell my tale. My Mongolian was now good enough to answer most questions and I tried to return the generous hospitality by entertaining my hosts with songs. Waltzing Matilda and Farewell to Botany Bay were popular but the biggest hit was Old MacDonald had a Farm. Translated into Mongolian it caused riotous laughter!

On reaching Tsetserleg, 410 km west of Ulaanbaatar, we rested for three days. My hosts had welcomed a new baby girl into the family a few days earlier and were delighted that I could join the celebrations.

Buddhist foundations. Only the retaining walls and three temples remain of the Erdene Zuu monastery (above), in Kharkhorin, which dates back to AD 1576. But Buddhism is undergoing a resurgence in Mongolia, and with limited funds, restoration of the remaining temples has begun. Graham spent three days helping a team of workers paint and in return, was allowed to graze Samson and Goliath in the knee-deep grass inside the temple walls. The running joke among the workers was how much the horses would benefit from eating such holy grass.

The approaching winter snows chased me from Tsetserleg through pine forests on the foothills of the Arkhangai Mountains as I wound my way through trees towards the former Mongol capital of Karakorum. I couldn't predict when winter, with all its harshness, would set in, but I could see the snowline, formerly a couple of hundred metres above me, getting closer.

Genghis Khan chose the fertile plains of this region to build his home, and the empire's capital. Today the walls and remaining three temples of the Erdene Zuu (Hundred Treasures) monastery are the most significant remains of this once-great city. The town fell into decay after the collapse of the Mongol empire, and is now run-down with poor facilities. I spent three days helping to paint some of the ancient temples, and in return received permission to graze the horses in the luscious knee-high grass inside the monastery walls. Needless to say, I had two very happy horses!

Karakorum, our last resting point before embarking on the 375 km leg back to Ulaanbaatar, was covered in a blanket of fresh snow when I left on 1 October. The horses were well rested and I'd stocked up on "essentials" like chocolate and dried bananas. As I travelled, the mountainous country slowly changed, with scattered rock piles and sparse vegetation giving it a barren look in comparison to the fertile north. My route took me past the Mongol Els, an unusual belt of desert sand dunes that stretches for 100 km and is surrounded by grassy steppe.