Context. Infrared dark clouds (IRDCs) can be the birth sites of high-mass stars, and hence determining the physical properties of dense cores in IRDCs is useful to constrain the initial conditions and theoretical models of high-mass star formation. Aims. We aim to determine the physical properties of dense cores in the filamentary Seahorse IRDC G304.74+01.32. Methods. We used data from the Wide-field Infrared Survey Explorer (WISE), Infrared Astronomical Satellite (IRAS), and Herschel in conjuction with our previous 350 and 870 μm observations with the Submillimetre APEX Bolometer Camera (SABOCA) and Large APEX BOlometer CAmera, and constructed the far-IR to submillimetre spectral energy distributions (SEDs) of the cores. The SEDs were fitted using single or two-temperature modified blackbody emission curves to derive the dust temperatures, masses, and luminosities of the cores. Results. For the 12 analysed cores, which include two IR dark cores (no WISE counterpart), nine IR bright cores, and one H II region, the mean dust temperature of the cold (warm) component, the mass, luminosity, H2 number density, and surface density were derived to be 13.3 ± 1.4 K (47.0 ± 5.0 K), 113 ± 29 M⊙, 192 ± 94 L⊙, (4.3 ± 1.2) × 105 cm−3, and 0.77 ± 0.19 g cm−3, respectively. The H II region IRAS 13039-6108a was found to be the most luminous source in our sample ((1.1 ± 0.4) × 103 L⊙). All the cores were found to be gravitationally bound (i.e. the virial parameter αvir < 2). Two out of the nine analysed IR bright cores (22%) were found to follow an accretion luminosity track under the assumptions that the mass accretion rate is 10−5 M⊙ yr−1, the stellar mass is 10% of the parent core mass, and the radius of the central star is 5 R⊙. Most of the remaing ten cores were found to lie within 1 dex below this accretion luminosity track. Seven out of 12 of the analysed cores (58%) were found to lie above the mass-radius thresholds of high-mass star formation proposed in the literature. The surface densities of Σ > 0.4 g cm−3 derived for these seven cores also exceed the corresponding threshold for high-mass star formation. Five of the analysed cores (42%) show evidence of fragmentation into two components in the SABOCA 350 μm image. Conclusions. In addition to the H II region source IRAS 13039-6108a, some of the other cores in Seahorse also appear to be capable of giving birth to high-mass stars. The 22 μm dark core SMM 9 is likely to be the youngest source in our sample that has the potential to form a high-mass star (96 ± 23 M⊙ within a radius of ~0.1 pc). The dense core population in the Seahorse IRDC has comparable average properties to the cores in the well-studied Snake IRDC G11.11-0.12 (e.g. Tdust and L agree within a factor of ~1.8); furthermore, the Seahorse, which lies ~60 pc above the Galactic plane, appears to be a smaller (e.g. three times shorter in projection, ~100 times less massive) version of the Snake. The Seahorse core fragmentation mechanisms appear to be heterogenous, including cases of both thermal and non-thermal Jeans instability. High-resolution follow-up studies are required to address the fragmented cores’ genuine potential of forming high-mass stars.