The broad traits of boldness and independence in domestic horses can affect their usefulness and, indirectly, their welfare. The objective of the current study was to explore associations between attributes that reflect equine boldness and independence with both the age of horses and the age at which they were started under saddle, as well as other variables including breed, colour and primary equestrian discipline. All data were sourced from responses (n = 1940) to the 97-question online Equine Behaviour Assessment and Research Questionnaire (E-BARQ). Twenty E-BARQ items from the dataset were selected to reflect boldness and independence and were tested for univariate significance at p < 0.2. Multivariable modelling of the effect of age on remaining traits was assessed by an ordinal logistic regression, using a cumulative log odds model. This revealed that older horses were bolder (p = 0.012). However, horses started under saddle at an older age were less bold and less independent (p = 0.040 and p = 0.010, respectively). Australian Stock Horses were bolder and more independent (p = 0.014 and p = 0.007, respectively) than crossbreed horses. Horses used for breeding conformation (p = 0.039), working equitation (p = 0.045), eventing (p = 0.044) and traditional working horses (p = 0.034) were bolder than those used for other disciplines. Dressage (p = 0.039) and therapy (p = 0.040) horses were less bold than horses used for other disciplines. Stallions were bolder (p = −0.034) than geldings. Brown (p = 0.049) and chestnut (p = 0.027) horses were less bold than bay horses. Compared to crossbreed horses, Thoroughbreds (p = 0.000) and companion horses (p = 0.017) were less bold whilst heavy horses (p = 0.029) and ponies (p = 0.044) were bolder. Compared to pleasure horses, mounted games horses (p = 0.033) were less independent whereas working equitation horses (p = 0.020) were more independent. Riders with more than eight years’ experience reported more independence in their horses (p = 0.015) than those who had ridden their whole lives. The study findings suggest that boldness and independence are separate traits and only boldness was associated with the age of the horse. Factors that relate to desirable boldness and independence are important in ridden horses because they can affect rider safety. Results from this study should improve horse–rider matching and thereby potentially enhance horse welfare.