Advice here ofc depence on what type attrition rules u use aka historic or normal.
For a beginner i would advice normal so ill use that.
First off u only lose cohesion when moving in/into a province u dont have military controll off.
So the only thing that could then cause u attrition in own territory is being outside a building in harsh weather = snow. So this is either u do or u dont situasion.
Is there any reasons to move or not. That will decide whether its worth teh risk + size of moving force. The larger ofc more casulties.
1 trick is move by rail and end in a building/structure, aka use the move into structure option. Since the check is made either before or after move, i ferget u can "island hop" from city to city via rail if ending in a strucktur u can avoid the winter attrition in own lands. The larger the struckture the bigger chance of avoiding hits.
As to move into province where u dont have military controll u will take a cohesion loss and since for movement: Hits are proportional to the cohesion cost of the move.)
Bad weather will do 2 things. Cohesion loss goes, up = more attrition, than non bad weather.
Apart from that u just like in own territory if not inside a build u get attrition weather based hits. Since movement takes longer u will be "outside" longer which in turn gives u more weather based hits.
In general that means i will suspend operations in the winter months atleased in area's of lesser concern. For example trying to take the North Arkansas hills in bad whether just going to make u die. Where an advance a single province in VA might be worth the risk. Its all very situasional. Just remember moving in bad weather and chances are that u cant make it into buildings "fast" u going to take lot of attrition hits so avoid it.
Ok that out of the way. This is my ways of dealing with cohesion.
Since in the eastern theather advances generally around much more than 1 max 2 provinces until u make contact there its more or less as u say damn the torpedoes full speed ahead. Assuming and this is importand that u are starting at full cohesion. If not i'd stop at leased one province before i hit teh enemy to stay there, regain cohesion and then advance again. Ofc u face teh risk of being counter attack, and not get the time to regain cohesion.
Still overall if u start with fresh troops and i generally try and make it that way. Moving 1, 2 provinces is fine, no problem. Damn the torpedoes full speed ahead.
In the west its some what different. More hills and the forces are in less direct contact. This mean i use in anticipating of combat or even moving up to a city to besiege it, the tactic of moving up too 1 province away from objective. Stay there and regain cohesion before attacking. Again depence on what ur starting cohesion and territory u pass through is. If u making a broad advance in no particular hurry. U can always use the advance 1 province at a time. Lets say u use 8 days on the move. Means remaining 7 days u rest and regain cohesion and u gain control of territory. Many times u can actually keep ur cohesion at max doing that(not counting through out the turn, but from turn to turn). At the same time u gain military control, which means u secure ur supply line. This is in it self essential if in a general advance.
As solowolf points out. Knowing which stances to use, when and when to be inside buildings to regain cohesion is importand to understand too. Luckily the tool tips on what u regain in which situasion is a much better teacher than words on a forum is. In my experience.
Hope it helps else ask away,
Rasmus