There'd be very little point in going all the way to Winchester when there were far closer strongholds at hand. Pop history tends to portray the Chippenham raid as this cataclysmic affair that almost sees Wessex entirely overrun, but that's very much not the case. At the same time as Chippenham is raided, a significant Danish fleet lands near Exeter, in what is most likely an attack aimed to coincide and capitalise on any upheaval caused by the Chippenham raid, but that army is met by the forwarned Devonshire fyrd and destroyed in detail. The following spring, when campaigning resumes, it's worth noting that Alfred's army at Eddington is comprised largely of the fyrds of Somerset, Wiltshire and Hampshire, which suggests that those counties felt that there was a sufficient lack of threat to commit manpower to that campaign. Alfred's decision to stay in Somerset was likely a PR decision, albeit one perhaps informed by a need for security since the fyrd would typically have been stood down over winter, and the Danes may still have been abroad. Staying with the Ealdorman and thegns of Somerset, however, would have been a useful opportunity to ensure that those areas remained loyal and felt that their king was sharing their hardships rather than being tempted to 'make peace' with the Danes on other terms.