The Herschel OB young stellar objects survey (HOBYS) has observed the Rosette molecular cloud, providing an unprecedented view of its star formation activity. These new far-infrared data reveal a population of compact young stellar objects whose physical properties we aim to characterise. We compiled a sample of protostars and their spectral energy distributions that covers the near-infrared to submillimetre wavelength range. These were used to constrain key properties in the protostellar evolution, bolometric luminosity, and envelope mass and to build an evolutionary diagram. Several clusters are distinguished including the cloud centre, the embedded clusters in the vicinity of luminous infrared sources, and the interaction region. The analysed protostellar population in Rosette ranges from 0.1 to about 15 M-circle dot with luminosities between 1 and 150 L-circle dot, which extends the evolutionary diagram from low-mass protostars into the high-mass regime. Some sources lack counterparts at near-to mid-infrared wavelengths, indicating extreme youth. The central cluster and the Phelps & Lada 7 cluster appear less evolved than the remainder of the analysed protostellar population. For the central cluster, we find indications that about 25% of the protostars classified as Class I from near-to mid-infrared data are actually candidate Class 0 objects. As a showcase for protostellar evolution, we analysed four protostars of low-to intermediate-mass in a single dense core, and they represent different evolutionary stages from Class 0 to Class I. Their mid-to far-infrared spectral slopes flatten towards the Class I stage, and the 160 to 70 mu m flux ratio is greatest for the presumed Class 0 source. This shows that the Herschel observations characterise the earliest stages of protostellar evolution in detail.