Millimeter-wave (mmWave) spectrum promises high throughput links for next-generation wireless agricultural networks, which will be characterized by teams of autonomous ground vehicles, unmanned aerial vehicles (UAVs), and connected agricultural machinery. However, channel models at mmWave frequencies in agricultural environments remain elusive. Moreover, due to the dynamic crop growth behavior, agricultural field channels bear notable distinctions from urban and rural macrocellular network channels. In this work, the most extensive agricultural field experiments on the mmWave spectrum are reported and a channel model is developed to characterize the large-scale path loss, coherence bandwidth, and link quality under the effect of various environmental factors. In particular, this study investigates the effects of wind on signal-to-noise ratio, and the diffuse scattering of electromagnetic waves due to near-canopy propagation at different crop growth stages. Accordingly, (1) during the growing season, the crop canopy surface acts as a 'new ground'. This new ground creates multipath components and results in a higher path loss exponent, which is correlated with the relative height between the crop canopy surface and the radios, (2) An increase of 4 m/s in gust speed results in a half-power drop (3-dB SNR degradation) due to beam misalignment and increased scattering, (3) the channel coherence bandwidth increases as the water content in the crop decreases, and (4) the beam-level spatial consistency allows for micro-mobility support for agricultural robotic applications. It is also shown that the impacts of humidity and water vapor on the mmWave channel are insignificant in the absence of rain and irrigation. Such characteristics are fundamental for designing advanced channel estimation and signal processing algorithms in advanced agricultural Internet-of-Things solutions. The extensive experiment dataset is made public for future reproducible research (https://ieeedataport.org/documents/mmwave-farm-channel-modelingwireless-agricultural-networks-broadband-millimeter-wave).